Statistical Inference

Problem 601

For the given confidence level and values of $x$ and $n$ , find the following. $x=44, n=96, \text { confidence level } 98 \%$
Part 1 of 3 (a) Find the point estimate. Round the answers to at least four decimal places, if necessary.
The point estimate for the given data is 0.4583 .
Part: $1 / 3$
Part 2 of 3 (b) Find the standard error. Round the answers to at least four decimal places, if necessary.
The standard error for the given data is $\square$

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Problem 602

iClicker Question Systolic blood pressures of healthy adults follow a normal distribution. We would like to conduct a hypothesis test at the $5 \%$ level of significance to determine if the true mean systolic blood pressure of healthy adults is greater than 120 . We take a random sample of 25 healthy adults. The sample mean systolic blood pressure is calculated to be 122 and the sample standard deviation is calculated to be 7.8. The P -value and conclusion of the appropriate test of significance are, respectively: (A) between 0.05 and 0.10 , fail to reject $\mathrm{H}_{0}$ . (B) between 0.10 and 0.15 , reject $\mathrm{H}_{0}$ . (C) between 0.10 and 0.15 , fail to reject $\mathrm{H}_{0}$ . (D) between 0.15 and 0.20 , reject $\mathrm{H}_{0}$ . (E) between 0.15 and 0.20 , fail to $\mathrm{H}_{0}$ .

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Problem 603

iClicker Question A scientist is concerned about radiation levels in her laboratory. A room is only considered safe if the mean radiation level is 425 or less. A random sample of 16 radiation measurements is taken at different locations within the laboratory. These 16 measurements have a mean of 437 and a standard deviation of 20. Radiation levels in the laboratory are known to follow a normal distribution. We conduct a hypothesis test at the $5 \%$ level of significance to determine whether there is evidence that the laboratory is unsafe.

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Problem 604

The Food and Drug Administration (FDA) regulates the amount of mercury in consumable fish, where consumable fish should only contain at most $1 \mathrm{mg} / \mathrm{kg}$ of mercury. In Florida, bass fish were collected in 51 different lakes to measure the amount of mercury in the fish from each of the 51 lakes. Do the data provide enough evidence to show that the fish in all Florida lakes have different mercury than the allowable amount? State the random variable, population parameter, and hypotheses. a. The symbol for the random variable involved in this problem is $\square$ $x-$ $\checkmark$ $0^{6}$ b. The wording for the random variable in context is as follows: the mercury level in fish of a randomly selected Florida lake Select an answer c. the mercury level in fish of a randomly selected Florida lake d. a randomly selected Florida lake the mean mercury level in fish of all Florida lakes the mean mercury level in fish of 51 randomly selected Florida lakes e. all Florida lakes the mercury level in fish 51 randomly selected Florida lakes f. A Type I error in the context of this problem would be
Rejecting that the mean mercury level in fish for all Florida lakes is $1 \mathrm{mg} / \mathrm{kg}$ when the mean really is $1 \mathrm{mg} / \mathrm{kg}$ .

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Problem 605

According to the Federal Trade Commission report on consumer fraud and identity theft, $23 \%$ of all complaints in 2007 were for identity theft. This year, a certain state kept track of the number of its 1415 complaints were for identity theft. They want to know if the data provide enough evidence to show that this state had a higher proportion of identity theft than $23 \%$ ? State the random variable, population parameter, and hypotheses. a. The symbol for the random variable involved in this problem is b. The wording for the random variable in context is as follows: Select an answer c. The symbol for the parameter involved in this problem is $\square$ $\square$ d. The wording for the parameter in context is as follows: Select an answer e. Fill in the correct null and alternative hypotheses. $\begin{array}{l} H_{0}: ? \vee ? v \square \\ H_{A}: ? \vee ? \vee \square \end{array}$ f. A Type I error in the context of this problem would be $\square$ g. A Type II error in the context of this problem would be
Select an answer Question Help: Video 1 Video 2 Submit Question

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Problem 606

Internet service: An Internet service provider sampled 538 customers and found that 78 of them experienced an interruption in high-speed service during the previous month.
Part 1 of 3 (a) Find a point estimate for the population of all customers who experienced an interruption. Round the answer to at least three decimal places.
The point estimate for the population proportion of all customers who experienced an interruption is 0.145 .
Part: $1 / 3$
Part 2 of 3 (b) Construct an $80 \%$ confidence interval for the proportion of all customers who experienced an interruption. Round the answer to at least three decimal places.
An $80 \%$ confidence interval for the proportion of all customers who experienced an interruption is $\square$ $<p<$ $\square$

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Problem 607

Volunteering: The General Social Survey asked 1305 people whether they performed any volunteer work during the past year. A total of 522 people said they did.
Part: $0 / 3$
Part 1 of 3 (a) Find a point estimate for the proportion of people who performed volunteer work during the past year. Round the answer to at least three decimal places.
The point estimate for the proportion of people who performed volunteer work during the past year is $\square$

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Problem 608

$\checkmark 3$ 14 $\checkmark 5$ 6 $\checkmark 7$ 8 9 10 $=11$ 12 13 14
WOW: In the computer game World of Warcraft, some of the strikes are critical strikes, which do more damage. Assume that the probability of a critical strike is the same for every attack, and that attacks are independent. During a particular fight, a character has 241 critical strikes out of 596 attacks.
Part: $0 / 3$ $\square$
Part 1 of 3 (a) Construct an $80 \%$ confidence interval for the proportion of strikes that are critical strikes. Round the answer to at least three decimal places.
An $80 \%$ confidence interval for the proportion of strikes that are critical strikes is $\square$ $<p<$ $\square$ .

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Problem 609

In a study of 789 randomly selected medical malpractice lawsuits, it was found that 484 of them were dropped or dismissed. Use a 0.05 significance level to test the claim that most medical malpractice lawsuits are dropped or dismissed.
Which of the following is the hypothesis test to be conducted? A. $\mathrm{H}_{0}: \mathrm{p}=0.5$ B. $H_{0}: p>0.5$ $H_{1}: p \neq 0.5$ $H_{1}: p=0.5$ C. $H_{0}: p \neq 0.5$ D. $H_{0}: p<0.5$ $H_{1}: p=0.5$ $H_{1}: p=0.5$ E. $H_{0}: p=0.5$ F. $\mathrm{H}_{0}: \mathrm{p}=0.5$ $H_{1}: p>0.5$ $H_{1}: p<0.5$
What is the test statistic? $z=6.37$ (Round to two decimal places as needed.) What is the P -value? P -value $=$ $\square$ (Round to three decimal places as needed.)

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Problem 610

Points: 0 of 1
A poll of 1137 Americans showed that $46.8 \%$ of the respondents prefer to watch the news rather than read or listen to it. Use those results with a 0.05 significance level to test the claim that fewer than half of Americans prefer to watch the news rather than read or listen to it. Use the P-value method. Use the normal distribution as an approximation to the binomial distribution.
Let p denote the population proportion of all Americans who prefer to watch the news rather than read or listen to it. Identify the null and alternative hypotheses. $\begin{array}{l|l} \mathrm{H}_{0}: \mathrm{p} & \mathbf{V} \\ \mathrm{H}_{1}: \mathrm{p} & \mathbf{7} \\ \hline \end{array}$ (Type integers or decimals. Do not round.)

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Problem 611

Part 1 of 4 Points: 0 of 1 Save
A poll of 1130 teens aged 13 to 17 showed that $53 \%$ of them have made new friends online. Use a 0.01 significance level to test the claim that half of all teens have made new friends online. Use the P -value method. Use the normal distribution as an approximation to the binomial distribution.
Let $p$ denote the population proportion of all teens aged 13 to 17 who have made new friends online. Identify the null and alternative hypotheses. $\begin{array}{l|l} \mathrm{H}_{0}: \mathrm{p} & \mathbf{Y} \\ \mathrm{H}_{1}: \mathrm{p} & \mathbf{Y} \\ \square \end{array}$ (Type integers or decimals. Do not round.)

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Problem 612

A sample tested the claim that heights of men and heights of women have difference variances, with $\mathrm{s}=7.47394 \mathrm{~cm}$ for women and 7.11392 cm for men. The sample sizes are $n_{1}=142$ and $n_{2}=157$ . When using the $F$ test with these data, is it correct to reason that there is no need to check for normality because $n_{1}>30$ and $n_{2}>30$ ?
Choose the correct answer below. A. Yes. The F test has a requirement that samples be from normally distributed populations, but this requirement can be ignored for large samples ( $n_{1}$ and $n_{2}$ greater than 30). B. No. The F test has a requirement that samples be from normally distributed populations, regardless of how large the samples are. C. No. There is no need to check for normality regardless of the sample size. There is no normality requirement for the F test. D. No. There is no need to check for normality as long as $n_{1} \geq 10$ and $n_{2} \geq 10$ .

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Problem 613

Based only on the analysis result here, what is the true nature of the relationship between English Score and Math Score?
Correlations \begin{tabular}{llr|r} & & EnglishScore & MathScore \\ \hline \multirow{3}{}{ EnglishScore } & Pearson Correlation & 1 & $.294^{}$ \\ \cline { 2 - 4 } & Sig. (2-tailed) & & .029 \\ \cline { 2 - 4 } MathScore & N & 55 & 55 \\ \cline { 2 - 4 } & Pearson Correlation & $.294^{}$ & 1 \\ \hline & Sig. (2-tailed) & .029 & \\ \cline { 2 - 4 } & N & 55 & 55 \\ \hline \end{tabular} . Correlation is significant at the 0.05 level (2-tailed). English ability significantly enhances math test performance. A generally high level of cognitive function enhances both english test scores and the math test scores. It's not possible to know the exact nature of the relationship based when one is only given the results of an analysis. Math ability significantly enhances English test performance.

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Problem 614

(a) $H_{0}: \mu=16, H_{a}: \mu=16$ This pair complies. This pair does not comply because $\mu$ is not a population characteristic. This pair does not comply because both hypotheses use an equal sign. This pair does not comply because the two hypotheses use different numbers. (b) $H_{0}: p=0.5, H_{a}: p>0.6$ This pair complies. This pair does not comply because $p$ is not a population characteristic. This pair does not comply because both hypotheses use an equal sign. This pair does not comply because the two hypotheses use different numbers.

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Problem 615

```latex The accompanying table lists distances (mm) between pupils of randomly selected U.S. Army personnel collected as part of a large reputable study. Results from two-way analysis of variance. Use the displayed results and use a 0.05 significance level. What do you conclude?
Click the icon to view the data and two-way analysis of variance results.
D. Fail to reject $\mathrm{H}_{0}$ . There is insufficient evidence to support the alternative hypothesis. There does not appear to be an interaction between gender and handedness.
If appropriate, test for an effect from the row factor. Choose the correct answer below.
A. $\mathrm{H}_{0}$ : Left-handed people and right-handed people have the same population mean distance between pupils. $\mathrm{H}_{1}$ : Left-handed people and right-handed people have different population mean distances between pupils.
B. $\mathrm{H}_{0}$ : Men and women have different population mean distances between pupils. $H_{1}$ : Men and women have the same population mean distance between pupils.
C. $\mathrm{H}_{0}$ : Left-handed people and right-handed people have different population mean distances between pupils. $\mathrm{H}_{1}$ : Left-handed people and right-handed people have the same population mean distance between pupils.
D. $\mathrm{H}_{0}$ : Men and women have the same population mean distance between pupils. $\mathrm{H}_{1}$ : Men and women have different population mean distances between pupils.
E. This test is not appropriate due to the results of the test for interaction between the two factors.
The user took a picture with their phone and the text was extracted above. The user then had a dialogue with an AI Assistant to help clarify the instructions.
Dialogue Transcript:
Hello! It looks like you have a two-way analysis of variance (ANOVA) problem here involving gender and handedness as factors. However, I need a bit more information to assist you properly. Could you please provide the specific results from the two-way ANOVA, such as the p-values for the main effects and interactions? Additionally, let me know if there is anything else specific you'd like help with regarding this problem.
Feel free to type out any important details that might help me understand the context better!
Extracted text from attached image:
Data and Two-Way ANOVA Results
\begin{tabular}{l|c|c} \hline & \text{Right-Handed} & \text{Left-Handed} \\ \hline \text{Female} & 6663596056 & 7162616962 \\ \hline \text{Male} & 6764666971 & 6767656864 \\ \hline \end{tabular}
\begin{tabular}{|lllllll|} \hline \text{Source:} & \text{DF:} & \text{SS:} & \text{MS:} & \text{Test Stat, F:} & \text{Critical F:} & \text{P-Value:} \\ \text{Interaction:} & 1 & 36.45 & 36.45 & 3.15584 & 4.49401 & 0.09467 \\ \text{Row Variable:} & 1 & 76.05 & 76.05 & 6.58442 & 4.49401 & 0.02072 \\ \text{Column Variable:} & 1 & 11.25 & 11.25 & 0.97403 & 4.49401 & 0.33837 \\ \hline \end{tabular} ```

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Problem 616

A large data set includes samples of body temperatures. Analyzing one sample of body temperatures results in $n=103, \bar{x}=98.19^{\circ} \mathrm{F}$ , and $\mathrm{s}=0.617^{\circ} \mathrm{F}$ . It is commonly believed that humans have a mean body temperature of $98.6^{\circ} \mathrm{F}$ . If the analysis is repeated with a different sample and it is found that for 100 randomly generated samples, 38 of these generated samples have a mean that is as extreme as the mean of the actual sample, what should be concluded about the assumed mean of $98.6^{\circ} \mathrm{F}$ ? (Assume that an event is significant if it has a probability of 0.05 or less.)
Since 38 of the 100 samples have means that are as much as the sample mean, then that sample mean $\square$ so there $\square$ strong evidence against the assumed mean of $98.6^{\circ} \mathrm{F}$ . It appears the population mean $\square$ $98.6^{\circ} \mathrm{F}$

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Problem 617

Are the snow conditions a factor in the number of visitors at a ski resort? The table below shows data that was collected. \begin{tabular}{|c|c|c|} \hline Hard Packed & Machine Made & Powder \\ \hline 1368 & 1804 & 1840 \\ \hline 1347 & 1552 & 1945 \\ \hline 2099 & 1676 & 1834 \\ \hline 2010 & 1945 & 1924 \\ \hline 2108 & 1810 & 2132 \\ \hline 1884 & 1571 & 1884 \\ \hline 1693 & 1534 & 1904 \\ \hline 1243 & 1006 & 1828 \\ \hline 2308 & & 2828 \\ \hline \end{tabular}
Assume that all distributions are normal, the three population standard deviations are all the same, and the data was collected independently and randomly. Use a level of significance of $\alpha=0.05$ . $H_{0}: \mu_{1}=\mu_{2}=\mu_{3}$ $H_{1}$ : At least two of the means differ from each other.
1. For this study, we should use Select an answer $\square$
2. The test-statistic for this data = $\square$ (Please show your answer to 3 decimal places.)
3. The $p$ -value for this sample $=$ $\square$ (Please show your answer to 4 decimal places.)
4. The $p$ -value is Select an answer $\square$ $\alpha$
5. Base on this, we should
Select an answer sion is that...
6. As such, the final conclusion is that... (0) hypothesis There is sufficient evidence to support the claim that snow conditions is a factor in the number of visitors at a ski resort. There is insufficient evidence to support the claim that snow conditions is a factor in the number of visitors at a ski resort.

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Problem 618

Find the line of best fit for the data: $(x, y) = (1, 9.6), (2, 6.3), (3, 2.8), (4, 8.73), (5, 5.9), (6, 1.2)$ . Interpret the correlation coefficient.

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Problem 619

The acceptable level for insect filth in a certain food item is 4 insect fragments (larvae, eggs, body parts, and so on) per 10 grams. A simple random sample of 60 ten-gram portions of the food item is obtained and results in a sample mean of $\bar{x}=4.8$ insect fragments per ten-gram portion. Complete parts (a) through (c) below. (a) Why is the sampling distribution of $x$ approximately normal? A. The sampling distribution of $\bar{x}$ is approximately normal because the population is normally distributed. B. The sampling distribution of $\bar{x}$ is approximately normal because the sample size is large enough. C. The sampling distribution of $\bar{x}$ is assumed to be i.pproximately normal, D. The sampling distribution of $\bar{x}$ is approximately normal because the population is normally distributed and the sample size is large enough. (b) What is the mean and standard deviation of the sampling distribution of $\bar{x}$ assuming $\mu=4$ and $\sigma=\sqrt{4}$ ? $\mu_{x}=$ $\square$ (Round to three decimal places as needed.) Get more help - Clear all Check answer

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Problem 620

$\begin{array}{r} H_{0}: \mu=0.8 \\ H_{1}: \mu \neq 0.8 \end{array}$
The null hypothesis in words would be: The proportion of people in a sample that prefers Trydint gum is 0.8 . The average of people that prefer Trydint gum is not 0.8. The proportion of all people that prefer Trydint gum is greater than 0.8 . The proportion of people in a sample that prefer Trydint gum is not 0.8 The proportion of all people that prefer Trydint gum is less than 0.8 . The average of people that prefer Trydint gum is 0.8 . The proportion of all people that prefer Trydint gum is 0.8
Based on a sample of 230 people, 167 said they prefer "Trydint" gum to "Eklypse". The point estimate is: $\square$ (to 3 decimals)
The $90 \%$ confidence interval is: $\square$ decimals) to $\square$ 385 Mostly cloudy

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Problem 621

If you are performing a right-tailed hypothesis test for a standard deviation, and you obtain a $\chi^{2}$ test statistic of 12.464 for a sample of size 6: (a) What conclusion would you reach when using a test with a significance level of 0.05 ?
Select an answer (b) What conclusion would be appropriate at a significance level of 0.01 ? Select an answer
Question Help: $\boldsymbol{\beta}^{-}$ Written Example Message instructor Check Answer

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Problem 622

Match each Test Situation with the correct Critical Value. For a two-sided test, find only the positive value. Test Situation Critical Value - $\vee$ One sample, $\mathrm{n}=45, H_{a}: p<p_{0}$ , and $\alpha=0.01$ a. 2.434 $-\vee$ One sample, $\mathrm{n}=61, H_{a}: p>p_{0}$ , and $\alpha=0.05$ b. 3.291 $-\vee$ One sample, $\sigma$ is known, $\mathrm{n}=175, H_{a}: \mu \neq \mu_{0}$ , and $\alpha=0.05$ c. 1.645 $-\vee$ One sample, $\sigma$ is unknown, $\mathrm{n}=57, H_{a}: \mu<\mu_{0}$ , and $\alpha=0.05$ d. 1.960 $-\vee$ One sample, $\sigma$ is unknown, $\mathrm{n}=37, H_{a}: \mu>\mu_{0}$ , and $\alpha=0.01$ e. -1.673 $-\vee$ One sample, $\mathrm{n}=35, H_{a}: p \neq p_{0}$ , and $\alpha=0.001$ f. 2.013 $-\checkmark$ One sample, $\sigma$ is unknown, $\mathrm{n}=47, H_{a}: \mu \neq \mu_{0}$ , and $\alpha=0.05$ g. -2.326
Question Help: $\square$ Message instructor Check Answer

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Problem 623

Question 15
You are conducting a study to see if the mean doctor's salary (in thousands of dollars) is significantly more than 87. A random sample of 26 doctors' salary in thousands of dollars is shown below. Test the claim using a $1 \%$ level of significance. Give answer to at least 4 decimal places. \begin{tabular}{|c|} \hline Salary \\ \hline 93.48 \\ \hline 80.66 \\ \hline 87.95 \\ \hline 93.93 \\ \hline 78.52 \\ \hline 81.63 \\ \hline 94.37 \\ \hline 94.89 \\ \hline 96.94 \\ \hline 95.55 \\ \hline 84.94 \\ \hline 83.74 \\ \hline 81.22 \\ \hline 93.16 \\ \hline 97.49 \\ \hline 88.39 \\ \hline 98.04 \\ \hline 87.34 \\ \hline 93.37 \\ \hline 84.99 \\ \hline 92.41 \\ \hline 91.7 \\ \hline 88.8 \\ \hline 87.61 \\ \hline 102.15 \\ \hline 93.73 \\ \hline \\ \hline \end{tabular} a. What are the correct hypotheses? $\mathrm{H}_{0}$ : $\square$ ? 2 $\square$ thousand dollars

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Problem 624

For the data below, determine the chi-squared value. Enter your value. Observed: 48 Expected: 50

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Problem 625

A job-placing agency claims that $73 \%$ of their clients find full-time jobs within a month of using their services. In a random sample of 170 people, it was found that $79 \%$ were able to find full-time employment within a month of joining the agency. Perform a test to determine whether more than $73 \%$ of the clientsfind full-time employment. Use a significance level of $2 \%$ . a. Check all of the requirements that are satisfied. random the $\boldsymbol{I}$ distribution is normal since $n \geq 30$ the $\boldsymbol{X}$ distribution is normal since the $\boldsymbol{X}$ distribution is normal the $\hat{p}$ distribution is normal since $n p \geq 10$ and $n q \geq 10$ b. Identify the null and alternative hypotheses. Enter the parameter as a decimal. $H_{0}$ : $\square$ $?$ $\qquad$ $\square$ $H_{1}$ : $\qquad$ $? \vee$ $\square$ c. What type of hypothesis test should you conduct (left, right, or two-tailed)? left-tailed right-tailed two-tailed d. Identify the appropriate significance level. Make sure to enter your answer as a decimal. $\square$ e. Which calculator function should you use? $\square$ f. Find the test statistic. Write the result below, and be sure to round your final answer to two decimal places. $\square$
8. Find the critical value. Round your answer to 2 decimal places. $\square$ h. Should you reject or not reject the null hypothesis? reject the null hypothesis since $p$ -value $\leq \alpha$ do not reject the null hypothesis since $p$ -value $>\alpha$ reject the null hypothesis since the test statistic is inside the critical region do not reject the null hypothesis since the test statistic is outside the critical region i. Select the statement below that best represents the interpretation. There is sufficient evidence to support the claim that more than $73 \%$ of the clients find fulltime employment within a month of joining the agency. There is not sufficient evidence to support the claim that more than $73 \%$ of the clients find full-time employment within a month of joining the agency. The sample data support the claim that more than 73\% of the clients find full-time employment within a month of joining the agency. We accept that more than $73 \%$ of the population find full-time employment within a month of joining the agency.

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Problem 626

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Current Attempt in Progress
Vitamin C for Sepsis. Sepsis occurs when a person's body has an overwhelmingly dangerous response to an infection. It can affect people of all ages and is life-threatening. Because vitamin C is believed to reduce inflammation, a randomized experiment ${ }^{1}$ was designed to see if intravenous administration of high-dose vitamin C would improve outcomes in patients with sepsis. Half the patients received an infusion of vitamin C while the other half received a placebo infusion. ${ }^{1}$ Fowler A, et al., "Effect of Vitamin C Infusion on Organ Failure and Biomarkers of Inflammation and Vascular Injury in Patients with Sepsis and Severe Acute Respiratory Failure," JAMA, 322(13), October 1, 2019.
Part 1
Your answer is correct. (a) Over a follow-up period of 28 days, the mean number of days on a ventilator was not significantly different between the two groups, while the mean number of days out of the Intensive Care Unit was significantly different. The $p$ -values for these two tests were 0.03 and 0.15 . Which $p$ -value goes with which test?
Ventilator test: 0.15 $\square$ ICU test: 0.03 $\square$ eTextbook and Media $\square$ Attempts: 1 of 5 used
Part 2 (b) Part (a) describes one test that was significant and one that wasn't in this study. In fact, many outcomes were measured and forty-six different tests were conducted. Forty-three of the 46 tests did not show a significant difference between the vitamin C group and the placebo group, while 3 did show significance at the $5 \%$ level. If vitamin Chas no effect, how many of the 46 tests do we expect to show significance just by random chance? (Do not round off your answer.) i

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Problem 627

Question 5 of 6 - /1 1 $z$ 3
A poll sampled 63 people, asking them their favorite skittle flavor by color (green, orange, purple, red, or yellow). A separate poll sampled 88 people, again asking them their favorite skittle flavor, but rather than by color they asked by the actual flavor (lime, orange, grape, strawberry, and lemon, respectively). The table below shows the results from both polls. Does the way people choose their favorite Skittles type, by color or flavor, appear to be related to which type is chosen? \begin{tabular}{lccccc} \hline & \begin{tabular}{c} Green \\ (Lime) \end{tabular} & \begin{tabular}{c} Purple \\ Orange \end{tabular} & \begin{tabular}{c} Red \\ (Grape) \end{tabular} & \begin{tabular}{c} Yellow \\ (Strawberry) \end{tabular} & \begin{tabular}{l} Lemon) \end{tabular} \\ \hline Color & 16 & 8 & 15 & 13 & 11 \\ Flavor & 13 & 16 & 20 & 31 & 8 \\ \hline \end{tabular}
Table 1 Skittles popularity (a) Give a table with the expected counts for each of the 10 cells.
Round your answers to one decimal place. \begin{tabular}{|c|c|c|c|c|c|} \hline & Green (Lime) & Orange & \begin{tabular}{l} Purple \\ (Grape) \end{tabular} & Red (Strawberry) & Yellow (Lemon) \\ \hline Color & i & i & i & i & i \\ \hline Flavor & i & i & i & i & i \\ \hline \end{tabular} (b) Are the expected counts large enough for a chi-square test? $\square$ (c) How many degrees of freedom do we have for this test?
Degrees of freedom $=$ $\square$ i (d) Calculate the chi-square test statistic.
Round your answer to two decimal places. chi-square statistic = $\square$ (e) Determine the $p$ -value.
Round your answer to three decimal places. p-value $=$ $\square$

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Problem 628

A stats instructor claims that their proportion of grades A's, B's, C's, and D's (this particular instructor doesn't give Fs) is as follows: $H_{o}: p_{A}=0.3 ; p_{B}=0.2 ; p_{C}=0.2 ; p_{D}=0.3$
Use a 0.005 significance level to test the instructor's claim. Complete the table. Report all answers accurate to three decimal places. \begin{tabular}{|c|l|ll||} \hline Category & \begin{tabular}{c} Observed \\ Frequency \end{tabular} & \multicolumn{1}{|c|}{\begin{tabular}{c} Expected \\ Frequency \end{tabular}} \\ \hline \hline A & 39 & 41.7 & $\checkmark$ \\ \hline B & 32 & $\sigma^{6}$ \\ \hline \hline C & 38 & 27.8 & $\checkmark$ \\ \hline \end{tabular}
What is the chi-square test-statistic for this data? $\chi^{2}=7.732 \quad x$
What is the Critical Value? C. V . $=$ 12.838 $\square$

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Problem 629

Question 7
Score on last try: 0.3 of 1 pts. See Details for more. Next question You can retry this question below
You are conducting a multinomial Goodness of Fit hypothesis test for the claim that all 5 categories are equally likely to be selected. Complete the table. Report all answers correct to three decimal places. \begin{tabular}{|c|c|c|c|} \hline Category & Observed Frequency & \begin{tabular}{l} Expected \\ Frequency \end{tabular} & $\frac{(O-E)^{2}}{E}$ \\ \hline A & 18 & & \\ \hline B & 24 & & \\ \hline C & 15 & & \\ \hline D & 20 & & \\ \hline E & 12 & & \\ \hline \end{tabular}

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Problem 630

You are conducting a multinomial hypothesis test $(\alpha=0.05)$ for the claim that all 5 categories are equally likely to be selected. Complete the table. \begin{tabular}{|c|c|c|c|} \hline Category & \begin{tabular}{l} Observed \\ Frequency \end{tabular} & \begin{tabular}{l} Expected \\ Frequency \end{tabular} & $\frac{(O-E)^{2}}{E}$ \\ \hline A & 6 & & \\ \hline B & 17 & & \\ \hline C & 6 & & \\ \hline D & 16 & & \\ \hline E & 18 & & \\ \hline \end{tabular}
Report all answers accurate to three decimal places. But retain unrounded numbers for future calculations.
What is the chi-square test-statistic for this data? (Report answer accurate to three decimal places, and remember to use the unrounded Pearson residuals in your calculations.) $\chi^{2}=$ $\square$ What are the degrees of freedom for this test?

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Problem 631

Savvas Realize Preview attachment...
You are conducting a multinomial hypothesis test $(\alpha=0.05$ ) for the claim that all 5 categories are equally likely to be selected. Complete the table. \begin{tabular}{|c|c|c|c|c|c|c|} \hline Category & Observed Frequency & \multicolumn{2}{|r|}{\begin{tabular}{l} Expected \\ Frequency \end{tabular}} & \multicolumn{3}{|l|}{ $\frac{(O-E)^{2}}{E}$ } \\ \hline A & 6 & 12.6 & & 3.457 & $\checkmark$ & 0 \\ \hline B & 17 & 12.6 & & 1.537 & $\checkmark$ & $0^{8}$ \\ \hline C & 6 & 12.6 & & 3.457 & $\checkmark$ & 06 \\ \hline D & 16 & 12.6 & & 0.917 & $\checkmark$ & 06 \\ \hline E & 18 & 12.6 & $\checkmark 0$ & 2.314 & $\checkmark$ & 06 \\ \hline \end{tabular}
Report all answers accurate to three decimal places. But retain unrounded numbers for future calculations.
What is the chi-square test-statistic for this data? (Report answer accurate to three decimal places, and remember to use the unrounded Pearson residuals in your calculations.) $\chi^{2}=11.682 \quad \checkmark 0^{\infty}$
What are the degrees of freedom for this test? d.f. $=$ $\square$ 4 0
What is the $p$ -value for this sample? (Report answer accurate to four decimal places.) p -value = $\square$ It may be best to use the =CHIDIST( ) function in a Spreadsheet to do this calculation. The $p$ -value is...

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Problem 632

You are conducting a multinomial hypothesis test ( $\alpha=0.05$ ) for the claim that all 5 categories are equally likely to be selected. Complete the table. \begin{tabular}{|c|c|c|c|} \hline Category & Observed Frequency & Expected Frequency & $\frac{(O-E)^{2}}{E}$ \\ \hline A & 20 & & \\ \hline B & 13 & & \\ \hline C & 12 & & \\ \hline D & 8 & & \\ \hline E & 24 & & \\ \hline \end{tabular}
Report all answers accurate to three decimal places. But retain unrounded numbers for future

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Problem 633

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Question 2 $0 / 1$ pt 5 99 Details
ANOVA is a statistical procedure that compares two or more treatment conditions for differences in variance. True False
Question Help: Written Example Post to forum Submit Question

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Problem 634

A researcher is interested in exploring the relationship between calcium intake and weight loss. Two different groups, each with 23 dieters, are chosen for the study. Group $A$ is required to follow a specific diet and exercise regimen, and also take a 500 -mg supplement of calcium each day, Group B is required to follow the same diet and exercise regimen, but with no supplemental calcium. After six months on the program, the members of Group A had lost a mean of 12.5 pounds with a standard deviation of 2.9 pounds. The members of Group B had lost a mean of 16.6 pounds with a standard deviation of 2.8 pounds during the same time period. Assume that the population variances are not the same. Construct a $90 \%$ confidence interval to estimate the true difference between the mean amounts of weight lost by dieters who supplement with calcium and those who do not. Let Population 1 be the amount of weight lost by Group A, who took a 500 -mg supplement of calcium each day, and let Population 2 be the amount of weight lost by Group B, who did not take a calcium supplement. Round the endpoints of the finterval to one decimal place, if necessary.
Answer Tables Keypad Keyboard Shortcuts

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Problem 635

Steve believes that his wife's cell phone battery does not last as long as his cell phone battery. On nine different occasions, he measured the length of time his cell phone battery lasted and calculated that the mean was 15.8 hours with a standard deviation of 3.1 hours. He measured the length of time his wife's cell phone battery lasted on twelve different occasions and calculated a mean of 24.2 hours with a standard deviation of 7.9 hours. Assume that the population variances are the same. Let Population 1 be the battery life of Steve's cell phone and Population 2 be the battery life of his wife's cell phone. Step 2 of 2: Interpret the confidence interval obtained in Step 1.
Answer Tables Keypad Keyboard Shortcuts Since the confidence interval contains zero, the data do not provide evidence that the population means are unequal at a $90 \%$ confidence level. We are $90 \%$ confident that the mean battery life of Steve's cell phone is between 3.6 hours and 13.2 hours shorter than the mean battery life of his wife's cell phone. We are $90 \%$ confident that the mean battery life of Steve's cell phone is between 3.6 hours and 13.2 hours longer than the mean battery life of his wife's cell phone. Since the confidence interval does not contain zero, the data do not provide evidence that the population means are unequal at a $90 \%$ confidence level.

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Problem 636

Is it worth pursuing a doctoral degree in education if you already have an undergraduate degree? One way to help make this decision is to look at the mean incomes of these two groups. Suppose that 11 people with bachelor's degrees in education were surveyed. Their mean annual salary was $\$ 45,000$ with a standard deviation of $\$ 6700$ . Sixteen people with doctoral degrees in education were found to have a mean annual salary of $\$ 40,500$ with a standard deviation of $\$ 5200$ . Assume that the population variances are not the same. Construct a $99 \%$ confidence interval to estimate the true difference between the mean salaries for people with doctoral degrees and undergraduate degrees in education. Let Population 1 be the salaries for people with doctoral degrees and Population 2 be the salaries for people with undergraduate degrees. Round the endpoints of the interval to the nearest whole number, if necessary. Tables Keypad Answer Keyboard Shortcuts

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Problem 637

Steve believes that his wife's cell phone battery does not last as long as his cell phone battery. On twelve different occasions, he measured the length of time his cell phone battery lasted and calculated that the mean was 22.3 hours with a standard deviation of 3.2 hours. He measured the length of time his wife's cell phone battery lasted on eight different occasions and calculated a mean of 15.9 hours with a standard deviation of 7.2 hours. Assume that the population variances are the same. Let Population 1 be the battery life of Steve's cell phone and Population 2 be the battery life of his wife's cell phone. Step 2 of 2: Interpret the confidence interval obtained in Step 1.
Answer Tables Keypad Keyboard Shortcuts Since the confidence interval does not contain zero, the data do not provide evidence that the population means are unequal at a $90 \%$ confidence level. We are $90 \%$ confident that the mean battery life of Steve's cell phone is between 2.3 hours and 10.5 hours shorter than the mean battery life of his wife's cell phone. We are $90 \%$ confident that the mean battery life of Steve's cell phone is between 2.3 hours and 10.5 hours longer than the mean battery life of his wife's cell phone. Since the confidence interval contains zero, the data do not provide evidence that the population means are unequal at a $90 \%$ confidence level.

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Problem 638

GUIDED SOLUTION
Essays A professor wishes to see if two groups of students' essays differ in lengths, that is, the number of words in each essay. The professor randomly selects 12 essays from a group of students who are science majors and 10 essays from a group of humanities majors to compare. The data are shown. At $\alpha=0.10$ , can it be concluded that there is a difference in the lengths of the essays between the two groups?
Science majors $\begin{array}{llllllllll} \text { Science majors } \\ \hline 2057 & 3129 & 2501 & 3464 & 2762 & 2075 & 2984 & 3783 & 3259 & 2389 \\ 3939 & 3425 \end{array}$
Humanities majors $\begin{array}{l} \text { Humanities majors } \\ \hline 2698 \\ \hline 2940 \\ 2257 \\ 19332 \\ 1740 \end{array}$
Send data to Excel Use $\mu_{1}$ for the mean of science majors and $\mu_{2}$ for the mean of humanities majors. Assume the populations are normally distributed, and that the variances are unequal. (a) State the hypotheses and identify the claim with the correct hypothesis. (b) Find the critical value(s). (c) Compute the test value. (d) Make the decision. (e) Summarize the results. (a) State the hypotheses and identify the claim with the correct hypothesis.
The null hypothesis $H_{0}$ is the statement that there is (Choose one) $\nabla$ between the means. This is equivalent to $\mu_{1}$ (Choose one) $\nabla \mu_{2}$ .

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Problem 639

\begin{align} &\text{Which of the following set of statements is true?} \\ &\text{1. About 94\% of the variation in daily temperature can be explained by a positive linear relationship with beach visitors.} \\ &\text{2. The correlation coefficient, } r, \text{ is } 0.880 \\ &\text{3. There is no strong correlation in the linear association between beach visitors and daily temperatures.} \\ &\text{4. The correlation coefficient, } r, \text{ is } 0.880 \\ &\text{5. About 94\% of the variation in beach visitors can be explained by a positive linear relationship with daily temperature.} \\ &\text{6. The correlation coefficient, } r, \text{ is } 0.969. \\ \end{align}

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Problem 640

Speeding Tickets A motorist claims that the South Boro Police issue an average of 60 speeding tickets per day. The following data show the number of speeding tickets issued each day for a period of one month. Assume $\sigma$ is 13.42 . Is there enough evidence to reject the motorist's claim at $\alpha=0.10$ ? Use the $P$ -value method. Assume the variable is normally distributed. \begin{tabular}{llllllll} 57 & 60 & 83 & 26 & 72 & 58 & 87 & 48 \\ 59 & 60 & 56 & 64 & 68 & 42 & 57 & 58 \\ 63 & 49 & 73 & 75 & 42 & 63 & 57 & 60 \\ 72 & 45 & & & & & & \end{tabular} Send data to Excel
Part: $0 / 5$
Part 1 of 5 (a) State the hypotheses and identify the claim. $\begin{array}{l} H_{0}: \square \text { (Choose one) } \nabla \\ H_{1}: \square \text { (Choose one) } \nabla \end{array}$
This hypothesis test is a (Choose one) $\boldsymbol{\nabla}$ test. $\square$

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Problem 641

Conduct the following test at the $\alpha=0.01$ level of significance by determining (a) the null and alternative hypotheses, (b) the test statistic, and (c) the critical value. Assume that the samples were obtained independently using simple random sampling. Test whether $\mathrm{p}_{1} \neq \mathrm{p}_{2}$ . Sample data are $\mathrm{x}_{1}=30, \mathrm{n}_{1}=255, \mathrm{x}_{2}=38$ and $\mathrm{n}_{2}=301$ . (a) Determine the null and alternative hypotheses. Choose the correct answer below. $H_{0}: p_{1}=p_{2}$ versus $H_{1}: p_{1}<p_{2}$ $H_{0}: p_{1}=p_{2}$ versus $H_{1}: p_{1}>p_{2}$ $H_{0}: p_{1}=p_{2}$ versus $H_{1}: p_{1} \neq p_{2}$

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Problem 642

Conduct a test at the $\alpha=0.05$ level of significance by determining (a) the null and alternative hypotheses, (b) the test statistic, and (c) the P-value. Assume the samples were obtained independently from a large population using simple random sampling. Test whether $p_{1}>p_{2}$ . The sample data are $x_{1}=129, n_{1}=241, x_{2}=135$ , and $n_{2}=312$ . (a) Choose the correct null and alternative hypotheses below. A. $H_{0}: p_{1}=p_{2}$ versus $H_{1}: p_{1}>p_{2}$ B. $H_{0}: p_{1}=p_{2}$ versus $H_{1}: p_{1} \neq p_{2}$ C. $H_{0}: p_{1}=p_{2}$ versus $H_{1}: p_{1}<p_{2}$ D. $H_{0}: p_{1}=0$ versus $H_{1}: p_{1} \neq 0$

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Problem 643

Part 1 of 4 Points: 0 of 1
In randomized, double-blind clinical trials of a new vaccine, monkeys were randomly divided into two groups. Subjects in group 1 received the new vaccine while subjects in group 2 received a control vaccine. After the second dose, 134 of 460 subjects in the experimental group (group 1) experienced drowsiness as a side effect. After the second dose, 26 of 84 of the subjects in the control group (group 2) experienced drowsiness as a side effect. Does the evidence suggest that a different proportion of subjects in group 1 experienced drowsiness as a side effect than subjects in group 2 at the $\alpha=0.01$ level of significance?
Determine the null and alternative hypotheses. Choose the correct answer below. A. $H_{0}: p_{1}=p_{2}$ versus $H_{1}: p_{1}<p_{2}$ B. $H_{0}: p_{1}=0$ versus $H_{0}: p_{1} \neq 0$ C. $H_{0}: p_{1}=p_{2}$ versus $H_{1}: p_{1} \neq p_{2}$ D. $H_{0}: p_{1}=p_{2}$ versus $H_{1}: p_{1}>p_{2}$

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Problem 644

Use the given statistics to complete parts (a) and (b). Assume that the populations are normally distributed. (a) Test whether $\mu_{1}>\mu_{2}$ at the $\alpha=0.05$ level of significance for the given sample data. (b) Construct a $99 \%$ confidence interval about $\mu_{1}-\mu_{2}$ . \begin{tabular}{ccc} & Population 1 & Population 2 \\ \hline $\mathbf{n}$ & 22 & 15 \\ \hline $\overline{\mathbf{x}}$ & 50.7 & 42.1 \\ \hline $\mathbf{s}$ & 4.6 & 10.6 \end{tabular} (a) Identify the null and alternative hypotheses for this test. A. $H_{0}: \mu_{1}=\mu_{2}$ B. $H_{0}: \mu_{1}>\mu_{2}$ C. $H_{0}: \mu_{1} \neq \mu_{2}$ $H_{1}: \mu_{1}<\mu_{2}$ $H_{1}: \mu_{1}=\mu_{2}$ $H_{1}: \mu_{1}=\mu_{2}$ D. $H_{0}: \mu_{1}<\mu_{2}$ E. $H_{0}: \mu_{1}=\mu_{2}$ F. $H_{0}: \mu_{1}=\mu_{2}$ $H_{1}: \mu_{1}=\mu_{2}$ $H_{1}: \mu_{1} \neq \mu_{2}$ $H_{1}: \mu_{1}>\mu_{2}$

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Problem 645

Question 1 0/1 pt 2 4
You measure 35 randomly selected textbooks' weights, and find they have a mean weight of 73 ounces. Assume the population standard deviation is 13.1 ounces. Based on this, construct a $90 \%$ confidence $90 \%$ interval for the true population mean textbook weight.
Give your answers as decimals, to two places $S=35$ < $\mu<$ $\qquad$

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Problem 646

Does failing to reject the null hypothesis mean that the null hypothesis is true? Explain.
Choose the correct answer. A. Yes. Failing to reject the null hypothesis means that there is enough evidence to reject it. B. No. Failing to reject the null hypothesis means that there is enough evidence to reject it. C. No. Failing to reject the null hypothesis means that there is not enough evidence to reject it. D. Yes. Failing to reject the null hypothesis means that there is not enough evidence to reject it.

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Problem 647

Identify a Type II error from these options: rejecting $H_0$ when $H_0$ is false, true, or not rejecting when true/false.

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Problem 648

What term describes findings in an experiment that reach conventional statistical significance? Options: nonsignificant, insignificant, significant, unworthy.

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Problem 649

Is there a link between liking a TV show and viewer age? (a) Find expected adults who dislike: $20.13$ . (b) Calculate $\chi^{2}$ test statistic: $\chi^{2}=\sum \frac{(observed - expected)^{2}}{expected}$ .

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Problem 650

1. We wish to improve yearling weight (YW) in our cow herd. $h^{2}$ for $\mathrm{WW}=.42$ mean of the selected bulls $=1130 \mathrm{lb}$ mean of all bulls $=1097 \mathrm{lb}$ mean of selected cows $=820 \mathrm{lb}$ mean of all cows $=813 \mathrm{lb}$ overall herd mean $=955 \mathrm{lb}$
Calculate: - Selection differential for: o Males - Females - Overall - Response to selection - New herd mean for YW

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Problem 651

\begin{enumerate} \item An office manager wants to determine if there is a relationship between the number of hours each week employees exercise and the number of sick days that they take each year. The data for the number of hours of exercise and sick days is given as follows: \begin{itemize} \item Hours of exercise: 1.5, 3, 2, 3.5, 2, 3.5, 4, 4.5, 2.5 \item Sick days: 16, 5, 9, 4, 12, 3, 2, 2, 11 \end{itemize} \item Find the correlation coefficient, $r$ . Round values to the nearest thousandth. \item Use the correlation coefficient and the scatter plot to determine if a relationship exists between these variables. Interpret this relationship. \item Can it be determined that this relationship is a cause-and-effect relationship? Why or why not? Are there other reasons this relationship might exist? If so, list some of these reasons. \end{enumerate}

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Problem 652

2. We wish to improve weaning weight (WW) in our cow herd. $h^{2}$ for $W W=.38$ herd mean for $W \mathrm{~W}=587 \mathrm{lb}$ \% saved (males) = 1 \% saved (females) = 15 Standard deviation for WW = 23 lb Calculate: - Overall selection intensity - Response to selection - Generation interval for: - Males - Females o Overall - Generation interval - Response per year
Assume we keep our cows for 9 calf crops starting at 2 years of age and we use our bulls for 3 calf crops starting at 2 years of age.

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Problem 653

Video: How to Find T-Value from a T-Table? t-table.pdf $\square$ What is the $t$ value with a $95 \%$ confidence interval for the true population mean if the sample size $\mathrm{n}=23$ ? (Please keep three decimal places) t value = $\square$ Submit Question

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Problem 654

Give the degrees of freedom for the chi-square test based on the two-way table. \begin{tabular}{l|llll|l} \hline & D & E & F & G & Total \\ \hline A & 39 & 34 & 43 & 34 & 150 \\ B & 78 & 89 & 70 & 93 & 330 \\ C & 23 & 37 & 27 & 33 & 120 \\ \hline Total & 140 & 160 & 140 & 160 & 600 \\ \hline \end{tabular}
Degrees of freedom $=$ $\square$

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Problem 655

\begin{tabular}{l|ccc|c} & HS & Some & College & Total \\ \hline Agree & 364 & 164 & 197 & 725 \\ Disagree & 558 & 471 & 787 & 1816 \\ \begin{tabular}{l} Don't \\ know \end{tabular} & 15 & 28 & 30 & 73 \\ \hline Total & 937 & 663 & 1014 & 2614 \\ \hline \end{tabular}
Table 1 Educational level and belief in One True Love
Round your answer for the chi-square statistic to one decimal place, and your answer for the $p$ -value to three decimal places. chi-square statistic $=$ $\square$ $p$ -value $=$ $\square$
Conclusion: $\square$ $H_{0}$ 。

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Problem 656

We say that the design of a study is biased if which of the following is true? (2) A racial or sexual preference is suspected. (b) Random placebos have been used. (c) Certain outcomes are systematically favored. (d) The correlation is greater than 1 or less than -1 . (e) An observational study was used when an experiment would have been feasible.

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Problem 657

5. A recent survey by a Canadian magazine on the contribution of universities to the economy was circulated to 394 people who the magazine decided "are the most likely to know how important universities are to the Canadian economy." Which of the following is the main problem with using these results to draw conclusions about the general public's perception? (a) Insufficient attention to the placebo effect. (b) $X 0$ control group. (c) Lack of random assignment. (d) Lack of random selection. (e) Response bias.

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Problem 658

estion 16 Time left 0:13:34
Given that $S_{x}^{2}=400, S_{y}^{2}=484, S_{x y}=350$ , and $n=10$ , the correlation coefficient is: 0.50 0.181 0.141 0.70 0.80 Next question

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Problem 659

zmianie dla innego poziomu istotności? i? \begin{tabular}{|c|c|c|c|c|c|c|c|c|c|} \hline Poziom cholesterolu przed kuracja & 225 & 236 & 312 & 238 & 241 & 196 & 205 & 259 & 218 \\ \hline Zad. 4. Warszawscy radni & 216 & 195 & 245 & 235 & 221 & 170 & 180 & 265 & 179 \\ \hline \end{tabular}

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Problem 660

Interpreting calculator display: The following TI-84 Plus display presents the results of a hypothesis test. ``` Z-Test \mu> > $5 z=2.872551059 P=.0020359269 \overline{x}}=48.7 n=71 ```
Part: $0 / 5$
Part 1 of 5
What are the null and alternate hypotheses? $\begin{array}{l|ll} H_{0}: \square & \square<\square & \square>\square \\ H_{1}: \square=\square \\ \square \neq \square & \mu \end{array}$

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Problem 661

Interpreting calculator display: The following TI-84 Plus display presents the results of a hypothesis test. ``` Z-Test \mu> $45 z}=2.87255105 P=.0020359269 \}=48.7 n=71 ```
Part: $0 / 5$ $\square$
Part 1 of 5 What are the null and alternate hypotheses? $\begin{array}{l} H_{0}: \mu=45 \\ H_{1}: \mu>45 \end{array}$
$\square$ $\square$ $1 \neq 1$ $\square$ $\mu$ $\square$ 0 lo $\square$ \%
Part: $1 / 5$
Part 2 of 5 What is the value of the test statistic? Enter the value to the full accuracy shown (do not round). $z=\square$

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Problem 662

Interpreting calculator display: The following TI-84 Plus display presents the results of a hypothesis test. \begin{tabular}{|l|} \hline \multicolumn{1}{|c|}{ z-Test } \\ $\mu>45$ \\ $z=2.872551059$ \\ $P=.0020359269$ \\ $\bar{x}=48.75$ \\ $n=71$ \end{tabular}
Part: $0 / 5$
Part 1 of 5
What are the null and alternate hypotheses? $\begin{array}{l} H_{0}: \mu=45 \\ H_{1}: \mu>45 \end{array}$ $\square$ $\infty$ do 탕
Part: $1 / 5$
Part 2 of 5
What is the value of the test statistic? Enter the value to the full accuracy shown (do not round). $z=2.87255105$ $\square$
Part: $2 / 5$
Part 3 of 5
What is the $P$ -value? Enter the value to the full accuracy shown (do not round). $P$ -value $=$ $\square$

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Problem 663

Free dessert: In an attempt to increase business on Monday nights, a restaurant offers a free dessert with every dinner order. Before the offer, the mean number of dinner customers on Monday was 150 . Following are the numbers of diners on a random sample of 12 days while the offer was in effect. Can you conclude that the mean number of diners decreased while the free dessert offer was in effect? Use the $\alpha=0.01$ level of significance and the $P$ -value method with the * Critical Values for the Student's t Distribution Table. \begin{tabular}{llllll} \hline 170 & 133 & 150 & 111 & 171 & 103 \\ 101 & 110 & 133 & 179 & 151 & 112 \\ \hline \end{tabular} Send data to Excel
Part: $0 / 6$
Part 1 of 6
Following is a boxplot for these data. Is it reasonable to assume that the conditions for performing a hypothesis test are satisfied? Explain.
The boxplot shows that there (Choose one) $\boldsymbol{\nabla}$ outliers. The boxplot shows that there (Choose one) $\boldsymbol{\nabla}$ evidence of strong skewness. We (Choose one) $\boldsymbol{\nabla}$ assume that the population is approximately normal. It (Choose one) $\nabla$ reasonable to assume that the conditions are satisfied.

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Problem 664

Free dessert: In an attempt to increase business on Monday nights, a restaurant offers a free dessert with every dinner order. Before the offer, the mean number of dinner customers on Monday was 150 . Following are the numbers of diners on a random sample of 12 days while the offer was in effect. Can you conclude that the mean number of diners decreased while the free dessert offer was in effect? Use the $\alpha=0.01$ level of significance and the $P$ -value method with the - ${ }^{-1}$ Critical Values for the Student's t Distribution Table. \begin{tabular}{llllll} \hline 170 & 133 & 150 & 111 & 171 & 103 \\ 101 & 110 & 133 & 179 & 151 & 112 \\ \hline \end{tabular} Send dáta to Excel
Part 1 of 6
Following is a boxplot for these data. Is it reasonable to assume that the conditions for performing a hypothesis test are satisfied? Explain.
The boxplot shows that there $\square$ outliers.
The boxplot shows that there $\square$ (Choose one) evidence of strong skewness. We (Choose one) $\square$ assume that the population is approximately normal. It $\square$ (Choose one) reasonable to assume that the conditions are satisfied. Part: 1 / 6 Part 2 of 6
State the appropriate null and alternate hypotheses. $\begin{array}{l} H_{0}: \square \\ H_{1}: \square \end{array}$
This hypothesis test is a $\square$ (Choose one) test.

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Problem 665

Free dessert: In an attempt to increase business on Monday nights, a restaurant offers a free dessert with every dinner order. Before the offer, the mean number of dinner customers on Monday was 150. Following are the numbers of diners on a random sample of 12 days while the offer was in effect. Can you conclude that the mean number of diners decreased while the free dessert offer was in effect? Use the $\alpha=0.01$ level of significance and the $P$ -value method with the
Critical Values for the Student's $t$ Distribution Table. \begin{tabular}{llllll} \hline 170 & 133 & 150 & 111 & 171 & 103 \\ 101 & 110 & 133 & 179 & 151 & 112 \\ \hline \end{tabular} Send data to Excel
Part 1 of 6
Following is a boxplot for these data. Is it reasonable to assume that the conditions for performing a hypothesis test are satisfied? Explain.
The boxplot shows that there are outliers. The boxplot shows that there is no evidence of strong skewness.
We can $\square$ assume that the population is approximately normal.
It $\square$ reasonable to assume that the conditions are satisfied.
Part 2 of 6
State the appropriate null and alternate hypotheses. $\begin{array}{l} H_{0}=\mu=150 \\ H_{1}: \mu<150 \end{array}$
This hypothesis test is a left-tailed $\square$ test. 5

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Problem 666

Free dessert: In an attempt to increase business on Monday nights, a restaurant offers a free dessert with every dinner order. Before the offer, the mean number of dinner customers on Monday was 150. Following are the numbers of diners on a random sample of 12 days while the offer was in effect. Can you conclude that the mean number of diners decreased while the free dessert offer was in effect? Use the $\alpha=0.01$ level of significance and the $P$ -value method with the - Critical Values for the Student's t Distribution Table. \begin{tabular}{llllll} \hline 170 & 133 & 150 & 111 & 171 & 103 \\ 101 & 110 & 133 & 179 & 151 & 112 \\ \hline \end{tabular} Send data to Excel Part 1 of 6
Following is a boxplot for these data. Is it reasonable to assume that the conditions for performing a hypothesis test are satisfled? Explain.
The boxplot shows that there $\square$ outliers.
The boxplot shows that there $\square$ is no evidence of strong skewness.
We $\square$ assume that the population is approximately normal.
It $\square$ reasonable to assume that the conditions are satisfied.
Part 2 of 6
State the appropriate null and alternate hypotheses. $\begin{array}{l} H_{0}: \mu=150 \\ H_{1}: \mu<150 \end{array}$ $\text { This hypothesis test is a left-tailed } \quad \nabla \text { test. }$
Part: $2 / 6$
Part 3 of 6
Compute the value of the test statistic. Round the answer to three decimal places. $t=-1.801$ $\square$ $\times$ 5 $\times$ 5 $\square$ $\infty$ (2) 目４） $\square$ alo 탕 I $\square$ $\begin{array}{l} 00 \quad 120 \quad 140 \quad 160 \quad 180 \\ 10 \end{array}$ $\qquad$

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Problem 667

Big babies: The National Health Statistics Reports described a study in which a sample of 322 one-year-old baby boys were weighed. Their mean weight was 25.1 pounds with standard deviation 5.3 pounds. A pediatrician claims that the mean weight of one-year-old boys is greater than 25 pounds. Do the data provide convincing evidence that the pediatrician's claim is true? Use the $\alpha=0.05$ level of significance and $P$ -value method with the (3) Critical Values for the Student's t Distribution Table.
Part: $0 / 5$ $\square$
Part 1 of 5 (a) State the appropriate null and alternate hypotheses. $\begin{array}{l} H_{0}: \square \\ H_{1}: \square \end{array}$
This hypothesis test is a (Choose one) $\nabla$ test. $\square$

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Problem 668

Heights ( cm ) and weights ( kg ) are measured for 100 randomly selected adult males, and range from heights of 139 to 193 cm and weights of 38 to 150 kg . Let the predictor variable x be the first variable given. The 100 paired measurements yield $\bar{x}=167.54 \mathrm{~cm}, \bar{y}=81.44 \mathrm{~kg}, \mathrm{r}=0.185, P$ -value $=0.065$ , and $\hat{y}=-107+1.05 x$ . Find the best predicted value of $\hat{y}$ (weight) given an adult male who is 161 cm tall. Use a 0.05 significance level.
Click the icon to view the critical values of the Pearson correlation coefficient $r$ .
The best predicted value of $\hat{y}$ for an adult male who is 161 cm tall is $\square$ kg . (Round to two decimal places as needed.)

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Problem 669

Do students perform the same when they take an exam alone as when they take an exam in a classroom setting? Eight students were given two tests of equal difficulty. They took one test in a solitary room and they took the other in a room filled with other students. The results are shown below.
Exam Scores \begin{tabular}{|c|c|c|c|c|c|c|c|c|} \hline Alone & 89 & 90 & 83 & 74 & 83 & 77 & 69 & 69 \\ \hline Classroom & 98 & 98 & 92 & 80 & 81 & 81 & 72 & 72 \\ \hline \end{tabular}
Assume a Normal distribution. What can be concluded at the the $\alpha=0.01$ level of significance level of significance?
For this study, we should use Select an answer a. The null and alternative hypotheses would be: $H_{0}$ : Select an answer Select an answer Select an answer $\square$ (please enter a decimal) $H_{1}$ : Select an answer Select an answer Select an answer (Please enter a decimal) b. The test statistic ? $=$ $\square$ (please show your answer to 3 decimal places.) c. The $p$ -value $=$ $\square$ (Please show your answer to 4 decimal places.) d. The $p$ -value is $\square$ $\alpha$ e. Based on this, we should Select an answer $\square$ t... f. Thus, the final conclusion is that the null hypothesis. The results are statistically insignificant at $\alpha=0.01$ , so there is insufficient evidence to conclude that the population mean test score taking the exam alone is not the same as the population mean test score taking the exam in a classroom setting. The results are statistically significant at $\alpha=0.01$ , so there is sufficient evidence to conclude that the population mean test score taking the exam alone is not the same as the population mean test score taking the exam in a classroom setting. The results are statistically significant at $\alpha=0.01$ , so there is sufficient evidence to conclude that the eight students scored the same on average taking the exam alone compared to the classroom setting. The results are statistically insignificant at $\alpha=0.01$ , so there is statistically significant evidence to conclude that the population mean test score taking the exam alone is equal to the population mean test score taking the exam in a classroom setting.

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Problem 670

You wish to test the following claim $\left(H_{a}\right)$ at a significance level of $\alpha=0.02$ . $\begin{array}{c} H_{o}: \mu=82.2 \\ H_{a}: \mu<82.2 \end{array}$
You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size $n=18$ with mean $M=78.3$ and a standard deviation of $S D=18.2$ .
What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic = $\square$ What is the p-value for this sample? (Report answer accurate to four decimal places.) p -value $=$ $\square$

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Problem 671

You wish to test the following claim $\left(H_{a}\right)$ at a significance level of $\alpha=0.02$ . $\begin{array}{l} H_{o}: \mu=50.3 \\ H_{a}: \mu<50.3 \end{array}$
You believe the population is normally distributed, but you do not know the standard deviation. You obtain the following sample of data: \begin{tabular}{|r|r|r|r|r|} \hline 56.1 & 21.7 & 24 & 61.8 & 55.5 \\ \hline 59.4 & 5.2 & 58 & 12.5 & 53.7 \\ \hline 69.4 & 18.9 & 54.3 & 36.8 & 45.3 \\ \hline 53.7 & 8.3 & 60.2 & 43.1 & 66.8 \\ \hline 40.8 & 44.9 & 69.4 & 20.8 & 32.4 \\ \hline 35.8 & 50.1 & 43.1 & 34.4 & 40.8 \\ \hline 35.8 & 39.1 & 28 & 44.9 & 40.4 \\ \hline 56.7 & 20.8 & 36.8 & 39.1 & 35.8 \\ \hline 39.1 & 31.4 & 12.5 & 31.4 & 71 \\ \hline 60.2 & 41.7 & 48.6 & 49.1 & 48.6 \\ \hline \end{tabular}
What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic = $\square$ What is the $p$ -value for this sample? (Report answer accurate to four decimal places.) p -value $=$ $\square$

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Problem 672

The "Freshman 15" refers to the belief that college students gain 15 lb (or 6.8 kg ) during their freshman year. Listed in the accompanying table are weights (kg) of randomly selected male college freshmen. The weights were measured in September and later in April. Use the listed paired sample data, and assume that the samples are simple random samples and that the differences have a distribution that is approximately normal. Complete parts (a) through (c). September $57 \quad 63 \quad 60$ 70 52 65 $\begin{array}{lll}74 & 92 & 57\end{array}$ April 58 65 64 68 53 82 92 59
Identify the P -value. P -value $=0.027^{7}$ (Round to three decimal places as needed.) What is the conclusion based on the hypothesis test? Since the P -value is less than the significance level, reject the null hypothesis. There is sufficient evidence to support the claim that for the population of freshman male college students, the weights in September are less than the weights in the following April. b. Construct the confidence interval that could be used for the hypothesis test described in part (a). What feature of the confidence interval leads to the same conclusion reached in part (a)?
The confidence interval is $\square$ $\mathrm{kg}<\mu_{\mathrm{d}}<$ $\square$ kg. (Type integers or decimals roundeध to one decimal place as needed.)

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Problem 673

Test the claim that the mean GPA of night students is smaller than 3.4 at the 0.025 significance level. The null and alternative hypothesis would be: $\begin{array}{cccccc} H_{0}: \mu \geq 3.4 & H_{0}: p=0.85 & H_{0}: p \leq 0.85 & H_{0}: p \geq 0.85 & H_{0}: \mu=3.4 & H_{0}: \mu \leq 3.4 \\ H_{1}: \mu<3.4 & H_{1}: p \neq 0.85 & H_{1}: p>0.85 & H_{1}: p<0.85 & H_{1}: \mu \neq 3.4 & H_{1}: \mu>3.4 \\ & & & & & \end{array}$
The test is: $\qquad$
Based on a sample of 80 people, the sample mean GPA was 3.37 with a standard deviation of 0.06 The test statistic is: $\square$ (to 2 decimals)
The $p$ -value is: $\square$ (to 2 decimals)

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Problem 674

$\begin{array}{c} H_{o}: \mu_{d}=0 \\ H_{a}: \mu_{d} \neq 0 \end{array}$
You believe the population of difference scores is normally distributed, but you do not know the standard deviation. You obtain the following sample of data: \begin{tabular}{|r|r|} \hline pre-test & post-test \\ \hline 28.9 & 30.1 \\ \hline 55.1 & 61.1 \\ \hline 39.6 & 37.4 \\ \hline 35.6 & -0.9 \\ \hline 52.5 & 49.6 \\ \hline 47.8 & 36.9 \\ \hline 45.3 & 31 \\ \hline 39.2 & 40.8 \\ \hline 36.5 & 37.3 \\ \hline 26.3 & 24.5 \\ \hline 44.5 & 8 \\ \hline 34.1 & 42.3 \\ \hline 35.1 & 61.3 \\ \hline 60.5 & 52.6 \\ \hline 50.7 & 49.3 \\ \hline 44.2 & 60.7 \\ \hline 52.1 & 80.9 \\ \hline \end{tabular}
What is the test statistic for this sample? test statistic $=$ $\square$ (Report answer accurate to 4 decimal places.)
What is the $p$ -value for this sample? p -value $=$ $\square$ (Report answer accurate to 4 decimal places.)

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Problem 675

he U.S. Department of Health has suggested that a healthy total cholesterol measurement should be $200 \frac{\mathrm{mg}}{\mathrm{dL}}$ or less. Records from 50 randomly and independently selected eople from a study conducted by the agency showed the results in the technology output given below. Test the hypothesis that the mean cholesterol level is more than 200 using a ignificance level of 0.05 . Assume that conditions are met.
One-Sample T Test of $\mu=200$ vs $>200$ \begin{tabular}{rrrrcc} N & Mean & StDev & SE Mean & T & P \\ 50 & 208.17 & 40.78 & 5.77 & 1.42 & 0.081 \\ \hline \end{tabular}
Determine the null and alternative hypotheses. Choose the correct answer below. A. $H_{0}: \mu=200$ B. $H_{0}: \mu=200$ C. $H_{0}: \mu<200$ $H_{a}: \mu>200$ $\mathrm{H}_{\mathrm{a}}: \mu \neq 200$ $H_{a}: \mu \geq 200$ D. $H_{0}: \mu>200$ E. $H_{0}: \mu=200$ F. $H_{0}: \mu \neq 200$ H. . 1 < mn H. . 1 < $20 n$ H. $"=2 \mathrm{mn}$ (1) Time Remaining: 01:25:23 Next

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Problem 676

A 2003 study of dreaming found that out of a random sample of 114 people, 85 reported drearning in color. However, the rate of reported drearning in color that was established in the 1940s was 0.28 . Check to see whether the conditions for using a one-proportion z-test are met assuming the researcher wanted to test to see if the proportion dreaming in color had changed since the 1940s.
Are the conditions met? A. No, the observations are not independent. B. No, the sample size is not large enough to produce at least 10 successes and 10 failures. C. No, the population is not more than 10 times bigger than the sample size. D. Yes, all the conditions are met.

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Problem 677

Suppose that, when taking a random sample of three students' GPAs, you get a sample mean of 3.90 . This sample mean is far higher than the college-wide (population) mean. Does this prove that your sample is biased? Explain. What else could have caused this high mean?
Choose the correct answer below. A. Nothing other than bias could have caused this small mean. B. The sample may not be biased. The measurements may not have been precise. C. One or more of the students could have lied about their GPAs. D. The sample may not be biased. The high mean might have occurred by chance, since the sample size is very small.

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Problem 678

According to a poll, 674 out of 1061 randomly selected smokers polled believed they are discriminated against in public life or in employment because of their smoking a. What percentage of the smokers polled believed they are discriminated against because of their smoking? b. Check the conditions to determine whether the CLT can be used to find a confidence interval. c. Find a $95 \%$ confidence interval for the population proportion of smokers who believe they are discriminated against because of their smoking. d. Can this confidence interval be used to conclude that the majority of smokers believe they are discriminated against because of their smoking? Why or why non? a. The percentage of those taking the poll believed they are discriminated against because of their smoking is (Round to one decimal place as needed.) $\square$ \%. b. Check the conditions to determine whether you can apply the CLT to find a confidence interval.
The Random and Independent condition $\square$ reasonably be assumed to hold. The Large Sample condition $\square$ The Big Population condition $\square$ c. The $95 \%$ confidence interval is $\square$ . ). (Round to three decimal places as needed.)

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Problem 679

A hospital readmission is an episode when a patient who has been discharged from a hospital is readmitted again within a certain time period. Nationally the readmission rate for patients with pneumonia is $19 \%$ . A hospital was interested in knowing whether their readmission rate for preumonia was less than the national percentage. They found 9 patients out of 60 treated for pneumonia in a two-month period were readmitted. Complete parts (a) through (d) below. c. Find the value of the test statistic and explain it in context.
The test statistic is $\square$ (Type an integer or a decimal rounded to two decimal places as needed.) The value of the test statistic tells that the observed proportion of readmissions was $\square$ $\square$ $\square$ the null hypothesis proportion of readmissions. (Type an integer or a decimal rounded to two decimal places as needed.) d. The p-value associated with this test statistic is 0.21 . Explain the meaning of the $p$ -value in this context. Based on this result, does the p-value indicate the null hypothesis should be doubted? Select the correct choice below and fill in the answer box within your choice. (Type an integer or a decimal. Do not round.) A. The probability of getting 9 or fewer readmissions for pneumonia of a random sample of 60 patients with preumonia is $\square$ . assuming the population proportion is less than 0.19. B. The probability of getting 9 or fewer readmissions for pneumonia of a random sample of 60 patients with pneumonia is $\qquad$ , assuming the population proportion is 0.19.

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Problem 680

A psychiatric nurse practitioner completes a study examining psychological distress scores, hours spent exercising, and number of counseling sessions to see if these variables impact minutes spent in ritualistic behavior among patients diagnosed with obsessive compulsive disorders. She reports the following information. \begin{tabular}{lll} & Beta & Sig \\ Psychological Distress & 3.98 & 0.040 \\ Exercise & -14.29 & 0.020 \\ Counseling Sessions & -1.45 & 0.031 \end{tabular}
If a patient engages in two hours of exercise what would you predict would happen to the number of minutes he/she spends in ritualistic behaviors? There would be no change in ritualistic behaviors The patient would engage in about 29 fewer minutes of ritualistic behaviors The patient would engage in about 15 minutes less of ritualistic behaviors. The patient would engage in about 20\% fewer minutes of ritualistic behaviors

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Problem 681

A researcher wants to compare the mean engagement score for nurses enrolled in graduate vs. undergraduate degree programs. What test would you recommend she utilize? repeat measures ANOVA T-test for independent groups Pearson's Correlation Coefficient. Logistic Regression

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Problem 682

Question 11 1 pts
A two-way chi square analysis provides the following data: Chi square-obt of 6.23 with 89 total participants.
What is the phi coefficient? $0.26$

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Problem 683

According to the manufacturer's data, $4.6 \%$ of the items coming off the production line have a defect. A random sample of size 25 was obtained. Let $\widehat{p}$ be the proportion of the sample that have a defect. Explain why the Central Limit Theorem cannot be used Select an answer

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Problem 684

Question 1. Assume that the following data set $\left\{\left(t, x_{t}\right)\right\}$ is from a stationary $\operatorname{AR}(1)$ time series with $\phi=0.78$ . \begin{tabular}{|c|c|c|c|c|c|c|c|c|} \hline $t$ & 1920 & 1925 & 1930 & 1935 & 1940 & 1945 & 1950 & 1955 \\ \hline $x_{t}$ & 0.112 & 0.88 & 0.68 & 0.53 & $?$ & 0.32 & $?$ & $?$ \\ \hline \end{tabular} a) Use the best linear predictor to estimate $x_{1940}$ using $x_{1935}$ . b) Use the best linear predictor to estimate $x_{1940}$ using $x_{1930}$ and $x_{1935}$ . c) Use the best linear predictor to estimate $x_{1940}$ using $x_{1935}$ and $x_{1945}$ . d) Use the best linear predictor to estimate $x_{1950}$ using $x_{1945}$ . e) Use the best linear predictor to estimate $x_{1955}$ .

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Problem 685

Assume that a simple random sample has been selected from a normally distributed population and test the given claim. Identify the null and alternative hypotheses, test statistic, P-value, and state the final conclusion that addresses the original claim. A safety administration conducted crash tests of child booster seats for cars. Listed below are results from those tests, with the measurements given in hic (standard head injury condition units). The safety requirement is that the hic measurement should be less than 1000 hic. Use a 0.05 significance level to test the claim that the sample is from a population with a mean less than 1000 hic. Do the results suggest that all of the child booster seats meet the specified requirement? $738$ 722 1238 648 566 570 A. $H_{0}: \mu=1000$ hic B. $H_{0}: \mu>1000$ hic $H_{1}: \mu \geq 1000$ hic $H_{1}: \mu<1000$ hic C. $H_{0}: \mu<1000$ hic D. $\mathrm{H}_{0}: \mu=1000$ hic $H_{1}: \mu \geq 1000$ hic $\mathrm{H}_{1}: \mu<1000$ hic
Identify the test statistic. $\mathrm{t}=$ $\square$ (Round to three decimal places as needed.)

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Problem 686

Essays A professor wishes to see if two groups of students' essays differ in lengths, that is, the number of words in each essay. The professor randomly selects 12 essays from a group of students who are science majors and 10 essays from a group of humanities majors to compare. The data are shown. At $\alpha=0.05$ , can it be concluded that there is a difference in the lengths of the essays between the two groups?
Science majors $\begin{array}{lllllllllllll}2262 & 3162 & 2450 & 3533 & 2725 & 1776 & 2830 & 3765 & 3357 & 2356 & 3887 & 3416\end{array}$ Humanities majors \begin{tabular}{llllllllll} 2604 & 2069 & 2123 & 1468 & 1952 & 2573 & 1886 & 2921 & 2237 & 2757 \end{tabular}
Send data to Excel Use $\mu_{1}$ for the mean of science majors and $\mu_{2}$ for the mean of humanities majors. Assume the populations are normally distributed, and that the variances are unequal.
Part 1 of 5 (a) State the hypotheses and identify the claim with the correct hypothesis. $\begin{array}{l} H_{0}: \mu_{1}=\mu_{2} \text { not claim } \\ H_{1}: \mu_{1} \neq \mu_{2} \text { claim } \end{array}$
This hypothesis test is a two-tailed $\quad$ test.
Part: $1 / 5$
Part 2 of 5 (b) Find the critical value. Round the answer(s) to at least three decimal places. If there is more than one critical value, separate them with commas.
Critical value(s): $\square$

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Problem 687

Essays A professor wishes to see if two groups of students' essays differ in lengths, that is, the number of words in each essay. The professor randomly selects 12 essays from a group of students who are science majors and 10 essays from a group of humanities majors to compare. The data are shown. At $\alpha=0.05$ , can it be concluded that there is a difference in the lengths of the essays between the two groups? Science majors \begin{tabular}{lllllllllllll} 2262 & 3162 & 2450 & 3533 & 2725 & 1776 & 2830 & 3765 & 3357 & 2356 & 3887 & 3416 \end{tabular}
Humanities majors $\begin{array}{llllllllll} \hline 2604 & 2069 & 2123 & 1468 & 1952 & 2573 & 1886 & 2921 & 2237 & 2757 \end{array}$
Send data to Excel
Use $\mu_{1}$ for the mean of science majors and $\mu_{2}$ for the mean of humanities majors. Assume the populations are normally distributed, and that the variances are unequal.
Part 1 of 5 (a) State the hypotheses and identify the claim with the correct hypothesis. $\begin{array}{l} H_{0}: \mu_{1}=\mu_{2} \text { not claim } \\ H_{1}: \mu_{1} \neq \mu_{2} \text { claim } \end{array}$
This hypothesis test is a two-tailed $\quad$ test.
Part 2 of 5 (b) Find the critical value. Round the answer(s) to at least three decimal places. If there is more than one critical value, separate them with commas.
Critical value(s): $2.262,-2.262$
Part: $2 / 5$
Part 3 of 5 (c) Compute the test value. Round your answer to at least three decimal places. $t=\square$

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Problem 688

Number of Farms A random sample of the number of farms (in thousands) in various states follows. Estimate the mean number of farms per state with $99 \%$ confidence. Assume $\sigma=31$ . Round intermediate and final answers to one decimal place. Assume the population is normally distributed. $\begin{array}{ccccccccccc} 4 & 64 & 33 & 54 & 95 & 47 & 50 & 40 & 109 & 78 & 6 \\ 52 & 21 & 15 & 7 & 68 & 16 & 48 & 79 & 44 & & \end{array}$ Send data to Excel $\square<\mu<\square$

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Problem 689

Predict heart weight (g) from body weight (kg) using regression.
(i) (a) Model: $\hat{y}=-0.339+4.028 x$ (b) Intercept: Expected heart weight at 0 kg is $-0.339$ g. (c) Slope: Each kg increases heart weight by 4.028 g. (d) $R^{2}$ : Body weight explains $64.65\%$ of heart weight variability. (e) Correlation coefficient: $0.8049$

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Problem 690

Calculate expected values under the null hypothesis for party affiliation and support of full-body scans.
(a) Expectation for Republicans not supporting: $48$ (b) Expectation for Democrats supporting: $?$ (c) Expectation for Independents unsure: $22$

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Problem 691

Analyze responses from 825 voters on oil drilling in CA. Perform a chi-square test for college grads vs non-grads at $\alpha = 0.05$ . State hypotheses, calculate test statistic (2 decimal places), and find $p$ -value (3 decimal places). Note data discrepancies.

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Problem 692

Survey skiers' preferences for ski areas. Test if preference is independent of skill level at $\alpha=0.05$ . Find test statistic and $p$ -value.

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Problem 693

A survey of 825 California voters examines opinions on offshore drilling. Perform a chi-square test with $H_{0}$ : no difference, $H_{A}$ : difference. Test statistic is 12.32; confirm and find the $p$ -value.

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Problem 694

Test if skier level and preferred ski area are independent at $\alpha = 0.05$ . Calculate test statistic, p-value, and conclusions.

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Problem 695

Find the slope of the best fit line for clubhead speeds (mph) and distances (yards) from 20 games data.

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Problem 696

Analyze the scatter plot of calories vs. fat in chicken sandwiches. What association is indicated by increasing grams and calories?

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Problem 697

Which aspect of a statistical study does the statement about cohabitation and divorce refer to: Inference, Design, or Description?

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Problem 698

A study of 27,000 individuals tested if a herbal supplement reduces asthma attacks. What aspects relate to design and description?

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Problem 699

What type of statistics is it when $90 \%$ of taste testers prefer the new coffee brand? Options: Investigation, Description, Design, Inference, None.

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Problem 700

A golfer has data on clubhead speeds (mph) and distances (yards) for 20 games. What analysis should be done: correlation, averages, or something else?

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Statistical Inference

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Problem 618

Find the line of best fit for the data: (x,y)=(1,9.6),(2,6.3),(3,2.8),(4,8.73),(5,5.9),(6,1.2)(x, y) = (1, 9.6), (2, 6.3), (3, 2.8), (4, 8.73), (5, 5.9), (6, 1.2)(x,y)=(1,9.6),(2,6.3),(3,2.8),(4,8.73),(5,5.9),(6,1.2). Interpret the correlation coefficient.

Problem 619

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Problem 624

For the data below, determine the chi-squared value. Enter your value. Observed: 48 Expected: 50

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Problem 633

Submit QuestionQuestion 2 0/10 / 10/1 pt 5 99 DetailsANOVA is a statistical procedure that compares two or more treatment conditions for differences in variance. True FalseQuestion Help: Written Example Post to forum Submit Question

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Problem 647

Identify a Type II error from these options: rejecting H0H_0H0​ when H0H_0H0​ is false, true, or not rejecting when true/false.

Problem 648

What term describes findings in an experiment that reach conventional statistical significance? Options: nonsignificant, insignificant, significant, unworthy.

Problem 649

Is there a link between liking a TV show and viewer age? (a) Find expected adults who dislike: 20.1320.1320.13. (b) Calculate χ2\chi^{2}χ2 test statistic: χ2=∑(observed−expected)2expected\chi^{2}=\sum \frac{(observed - expected)^{2}}{expected}χ2=∑expected(observed−expected)2​.

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Problem 653

Video: How to Find T-Value from a T-Table? t-table.pdf □\square□ What is the ttt value with a 95%95 \%95% confidence interval for the true population mean if the sample size n=23\mathrm{n}=23n=23 ? (Please keep three decimal places) t value = □\square□ Submit Question

Problem 654

Problem 655

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Problem 658

estion 16 Time left 0:13:34Given that Sx2=400,Sy2=484,Sxy=350S_{x}^{2}=400, S_{y}^{2}=484, S_{x y}=350Sx2​=400,Sy2​=484,Sxy​=350, and n=10n=10n=10, the correlation coefficient is: 0.50 0.181 0.141 0.70 0.80 Next question

Problem 659

zmianie dla innego poziomu istotności? i? \begin{tabular}{|c|c|c|c|c|c|c|c|c|c|} \hline Poziom cholesterolu przed kuracja & 225 & 236 & 312 & 238 & 241 & 196 & 205 & 259 & 218 \\ \hline Zad. 4. Warszawscy radni & 216 & 195 & 245 & 235 & 221 & 170 & 180 & 265 & 179 \\ \hline \end{tabular}

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Problem 670

Find the line of best fit for the data: $(x, y) = (1, 9.6), (2, 6.3), (3, 2.8), (4, 8.73), (5, 5.9), (6, 1.2)$ . Interpret the correlation coefficient.

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Question 2 $0 / 1$ pt 5 99 Details
ANOVA is a statistical procedure that compares two or more treatment conditions for differences in variance. True False
Question Help: Written Example Post to forum Submit Question

Identify a Type II error from these options: rejecting $H_0$ when $H_0$ is false, true, or not rejecting when true/false.

Is there a link between liking a TV show and viewer age? (a) Find expected adults who dislike: $20.13$ . (b) Calculate $\chi^{2}$ test statistic: $\chi^{2}=\sum \frac{(observed - expected)^{2}}{expected}$ .

Video: How to Find T-Value from a T-Table? t-table.pdf $\square$ What is the $t$ value with a $95 \%$ confidence interval for the true population mean if the sample size $\mathrm{n}=23$ ? (Please keep three decimal places) t value = $\square$ Submit Question

estion 16 Time left 0:13:34
Given that $S_{x}^{2}=400, S_{y}^{2}=484, S_{x y}=350$ , and $n=10$ , the correlation coefficient is: 0.50 0.181 0.141 0.70 0.80 Next question