Data & Statistics

Problem 501

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14 Multiple Choice 3.5 points Courses
$14 / 39$ Calendar
-11.4\%
$-12 \%$
$12 \%$ $11.4 \%$

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Problem 502

The pulse rates of 176 randomly selected adult males vary from a low of 39 bpm to a high of 111 bpm . Find the minimum sample size required to estimate the mean pulse rate of adult males. Assume that we want $95 \%$ confidence that the sample mean is within 4 bpm of the population mean. Complete parts (a) through (c) below. a. Find the sample size using the range rule of thumb to estimate $\sigma$ . $n=$ $\square$ (Round up to the nearest whole number as needed.)

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Problem 503

A data set includes 103 body temperatures of healthy adult humans having a mean of $98.3^{\circ} \mathrm{F}$ and a standard deviation of $0.73^{\circ} \mathrm{F}$ . Construct a $99 \%$ confidence interval estimate of the mean body temperature of all healthy humans. What does the sample suggest about the use of $98.6^{\circ} \mathrm{F}$ as the mean body temperature? Click here to view a t distribution table. Click here to view page 1 of the standard normal distribution table. Click here to view page 2 of the standard normal distribution table.
What is the confidence interval estimate of the population mean $\mu$ ? $\square$ $\square$ ${ }^{\circ} \mathrm{F}<\mu<\square^{\circ} \mathrm{F}$ (Round to three decimal places as needed.)

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Problem 504

$\begin{array}{c} \text { P(hsuccesses })=n^{C} p^{n}(1-\rho)^{n-h} \\ n^{B}=\frac{n!}{(n-h)|h|} \end{array}$ ${ }_{7} C_{5}\left(\frac{1}{6}\right)^{2}\left(\frac{1}{6}\right)^{5}$ ${ }_{7} C_{5}\left(\frac{1}{6}\right)^{5}\left(\frac{5}{6}\right)^{2}$ ${ }_{7} \mathrm{C}_{2}\left(\frac{1}{6}\right)^{2}\left(\frac{5}{6}\right)^{5}$ ${ }_{7} C_{2}\left(\frac{2}{6}\right)^{2}\left(\frac{4}{6}\right)^{5}$

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Problem 505

Consider the following monthly amortization schedule: \begin{tabular}{|c|c|c|c|c|} \hline Payment \# & Payment & Interest & Debt Payment & Balance \\ \hline 1 & 996.45 & 750.00 & 216.45 & $149,783.55$ \\ \hline 2 & 996.45 & 748.92 & 217.53 & $149,566.02$ \\ \hline 3 & 996.45 & & & \\ \hline \end{tabular}
With the exception of column one, all amounts are in dollars. Calculate the annual interest rate on this loan.

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Problem 506

4. In the United States, it is well-known that for the population of males, the mean height is 69.1 inches with standard deviation 4 inches. A researcher believes that a certain group is significantly taller than other males, due to genetic factors. For a sample of 25 such men, the mean is 71.2 inches with standard deviation 3.5 inches. a. Can it be reasonably assumed that the population is normally distributed? Are the criteria met to perform a z-test for the mean? Explain. b. Set up the null and alternative hypothesis to test if this population is taller than average. c. Calculate the value of the test statistic. d. Find the p-value. e. At the $5 \%$ level of significance $(\alpha=0.05)$ , make a decision whether to reject $H_{0}$ . f. What can we conclude?

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Problem 507

for a manturing company wishes to reduce the mean time needed serer visit to a customer location in his region. Nationally, this company sets a standard that a customer service visit should last at most four hours, on average. He is concerned that the service technicians in his region may be violating that standard, so he samples 41 customer service visits. In this sample, the mean time needed for a service visit is 4.2 hours with standard deviation 1.6 hours. In a previous example, we determined that the $t$ -test for the mean should be conducted. a. Set up the null and alternative hypothesis to test the regional manager's claim that the standard set by the company is being violated. b. Calculate the value of the test statistic. c. Find the p-value. d. At the $\alpha=0.05$ level of significance, make a decision whether to reject $\mathrm{H}_{0}$ . e. Interpret this conclusion.

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Problem 508

A certain game involves tossing 3 fair coins, and it pays $9 \notin$ for 3 heads, $4 \notin$ for 2 heads, fand $2 \notin$ for 1 head. Is $4 \notin$ a fair price to pay to play this game? That is, does the $4 \phi$ cost to play make the game fair?
The $4 c$ cost to play $\square$ is not a fair price to pay because the expected winnings are $\square$ 4. (Type an integer or a fraction. Simplify your answer.)

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Problem 509

Sec 9.4 Rare Events, the
1. At significance level $\alpha=0.10$ , determine if the null hypothesis should be rejected given the test statistic and p -value. 1 A manufacturer of automobile batteries claims that the average life of its best battery is 54 months. A consumer advocacy group believes that this might be incorrect. The test statistic is found to be -7.07 and the p -value is $\approx 0$ .

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Problem 510

Ten thousand raffle tickets are sold. One first prize of $\$ 1000$ , two second prizes of $\$ 750$ , and three third prizes of $\$ 200$ each will be awarded, with all winners selected randomly. If you purchased one ticket, what are your expected gross winnings?
The expected gross winnings are $\square$ cents. (Round your answer to the nearest whole cent.)

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Problem 511

2. At significance level $\alpha=0.10$ , determine if the mull hy pothesis should be rejected given the test statistic and p-value. Interpret the result. a. The FDA mandates that the average number of rodent hairs in a sumple of apple butter be no more than 4 hairs. A consumer advocacy group claims that a cerrain brand is violating this standard. The test statistic is found to be 294 and the p-value is 0.0016. b. A report states that doctors are late for $12 \%$ of all appointments. A doctor claims that less than $12 \%$ of his appointments are taken late. The test statistic is found to be -0.44 and the p -value is 0.3299 . c. A company claims it has redesigned light bulbs to last longer. The previous design had an average life of 1200 hours. The test statistic is 2.08 and the $p$ -value is 0.0188

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Problem 512

3. Psychologists were interested in the physiological changes that occur when a person laughed. The subjects in the study watched videos to encourage laughter. While the subjects were laughing, the researchers measured the subject's pulse. In a sample of 90 subjects, the mean heart rate was 73.5 beats per minute (bpm) with standard deviation 6 bpm . The mean resting heart rate of the population of all adults is known to be 71 bpm with standard deviation 7.5 bpm . The researchers wish to determine if the mean heart rate is elevated during laughter. In a previous example, we determined that the z -test for the mean should be conducted. a. Set up the null and alternative hypothesis for this test. b. Calculate the value of the test statistic. c. Find the p-value. d. At the $\alpha=0.05$ level of significance, make a decision whether to reject $\mathrm{H}_{0}$ . e. Can it be determined that the mean heart rate is elevated during laughter?

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Problem 513

5. At a certain government agency, all employees must undergo a training course and take an online quiz to assess their knowledge. The completion time for the population of all government employees who take the quiz is normally distributed with mean 32 minutes and standard deviation 13 minutes. It is suspected that one group of employees cheated on the quiz, since their completion time was shorter than average. In this sample of 34 employees, the mean completion time was 29 minutes with standard deviation 4 minutes. At the $\alpha=0.05$ level of significance, what can be concluded? Include the following steps in your test. - State the null and alternative hypotheses - Calculate the test statistic - Find the p-value - Make a decision whether to reject $\mathrm{H}_{0}$ - Write an interpretation of the results

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Problem 514

7. It is reported that a stock price for a particular company will grow at a mean rate of $\$ 5$ per week. An investor believes that this report is not accurate. The changes in stock prices are recorded for ten weeks and the data appear below. Assume the population is normally distributed. \ $4 \$3 \$2 \$3 \$1 \$7 \$2 \$1 \$1 \$2 a. Verify that the conditions for the$ t $-test for the mean are satisfied. b. Set up the null and alternative hypothesis to test the investor's claim. c. Calculate the value of the test statistic. d. Find the$ p $-value. e. At the$ 5 \% $level of significance$ (\alpha=0.05) $, make a decision whether to reject$ H_{0}$.

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Problem 515

$\text{Use the graph at right to answer the following questions.}$ $\text{What is the monopolist's profit-maximizing output?} \, \square$
\text{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.}
\text{Dialogue Transcript:}
\text{Hi there! It looks like you have a question about finding the monopolist's profit-maximizing output using a graph. However, it seems like some crucial information is missing, specifically the graph itself.}
\text{To help you determine the profit-maximizing output, I need to know more about the graph, such as:}
\begin{itemize} \item \text{The demand curve} \item \text{The marginal cost curve} \item \text{The marginal revenue curve} \end{itemize}
\text{Could you provide a description of these elements, or alternatively, any details you can see from the graph? Once I have that information, I will be able to guide you through finding the monopolist's profit-maximizing output.}
\text{The marginal cost is the MC on the graph. The marginal revenue is the MR on the graph and the demand curve is the D on the graph.}

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Problem 516

\begin{problem} The table below shows information about the masses of some dogs:
\begin{tabular}{|r|c|} \hline \text{Mass, } x(\mathrm{~kg}) & \text{Frequency} \\ \hline 0 \leq x < 10 & 2 \\ \hline 10 \leq x < 20 & 7 \\ \hline 20 \leq x < 30 & 12 \\ \hline 30 \leq x < 40 & 6 \\ \hline \end{tabular}
\begin{enumerate} \item[(a)] Work out the minimum number of dogs that could have a mass of more than 24 kg. \item[(b)] Work out the maximum number of dogs that could have a mass of more than 24 kg. \end{enumerate} \end{problem}

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Problem 517

Dreams Recalled during One Week \begin{tabular}{|l|c|c|c|c|} \hline & None & 1 to 4 & 5 or more & Total \\ \hline Group X & 15 & 28 & 57 & 100 \\ \hline Group Y & 21 & 11 & 68 & 100 \\ \hline Total & 36 & 39 & 125 & 200 \\ \hline \end{tabular}
The data in the table above were produced by a sleep researcher studying the number of dreams people recall when asked to record their dreams for one week. Group X consisted of 100 people who observed early bedtimes, and Group Y consisted of 100 people who observed later bedtimes. If a person is chosen at random from those who recalled at least 1 dream, what is the probability that the person belonged to Group $\mathrm{Y}^{\prime}$ ? A) $\frac{68}{100}$ B) $\frac{79}{100}$ C) $\frac{79}{164}$ D) $\frac{164}{200}$

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Problem 518

The city of Raleigh has 10,500 registered voters. There are two candidates for city council in an upcoming election: Brown and Feliz. The day before the election, a telephone poll of 350 randomly selected registered voters was conducted. 130 said they'd vote for Brown, 199 said they'd vote for Feliz, and 21 were undecided.
Use this information from the sample to complete the following statements about the population of all registered voters in Raleigh. Round your answers to the nearest person.
Based on this sample, we could expect 3,900 $0^{8} 3900$ of the 10,500 registered voters to vote for Brown.
Based on this sample, we could expect $\square$ of the 10,500 registered voters to vote for Feliz. Based on this sample, $\square$ of the 10,500 registered voters are still undecided.
Question Help: Video Message instructor Submit Question

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Problem 519

Explain the meaning of the law of large numbers. Does this law say anything about what will happen in a single observation or experiment? Why or why not?
Explain the meaning of the law of large numbers. Choose the correct answer below A. As the experiment is done more and more times, the experimenter learns how to do the experiment better. Therefore the number of outcomes should start to match the theoretical probability. B. The theoretical probability is more accurate if it involves large numbers. C. As the experiment is done more and more times, the proportion of times that a certain outcome occurs should get closer to the theoretical probability that that outcome would occur. D. If an experiment is conducted 1000 times, the probability that a certain outcome occurs should become more predictable than if it was conducted 1500 times.

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Problem 520

22. When the price of an inferior good rise, the substitution effect $\qquad$ the quantity demanded and the income effect $\qquad$ the quantity demanded. A. Decreases; decreases B. Decreases; increases C. Increases; decreases D. Increases; increases sis $x^{2}$ J 1 (o)
Normal

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Problem 521

Let $x$ be a continuous random variable that follows a normal distribution with a mean of 200 and a standard deviation of 25 . Find the value of $x$ so that the area under the normal curve to the right of $x$ is 0.7967 .
Round your answer to two decimal places. $x=$ $\square$

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Problem 522

14. If $o\left(E^{\prime}\right)=9: 11$ , find $p(E)$ .
15. Find the probability of choosing 7 winning spots in nine-spot keno.

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Problem 523

16. A pen manufacturer gets its pen cartridges from 2 suppliers. $58 \%$ of the cartridges come from supplier A and $2.25 \%$ of them are defective. $42 \%$ of the cartridges come from supplier B and $1.75 \%$ of them are defective. Answer the following questions: (a) Draw a tree diagram representing the problem. (b) Find the probability that a cartridge is defective and from supplier A. (c) Find the probability that a randomly chosen cartridge is not defective.

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Problem 524

According to the records of an electric company serving the Boston area, the mean electricity consumption during winter for all households is 1650 kilowatt-hours per month. Assume that the monthly electricity consumption during winter by all households in this area have a normal distribution with a mean of 1650 kilowatt-hours and a standard deviation of 320 kilowatt-hours. The company sent a notice to Bill Johnson informing him that about $75 \%$ of the households use less electricity per month than he does. What is Bill Johnson's monthly electricity consumption? Round your answer to the nearest integer. Bill Johnson's monthly electricity consumption is approximately $\square$ kWh. eTextbook and Media

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Problem 525

Complete the table shown to the right for the population growth model for a certain country. \begin{tabular}{|c|c|c|} \hline 2006 Population(millions) & Projected 2030 Population (millions) & Projected Growth Rate, k \\ \hline 77.9 & & 0.0172 \\ \hline \end{tabular} he projected 2030 population is $\square$ million. zound to one decimal place as needed.)

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Problem 526

$\text{Calculate the average grade for the user based on the given 6-week periods. The grades are as follows:}$ \begin{align} \text{1st 6 Weeks:} & \quad 94\% \, (A), \, 93\% \, (A), \, 90\% \, (A), \, 78\% \, (C), \, 71\% \, (C), \, 65\% \, (D) \\ \text{2nd 6 Weeks:} & \quad 60\% \, (D), \, 70\% \, (C), \, 61\% \, (D) \\ \text{3rd 6 Weeks:} & \quad 100\% \, (A), \, 72\% \, (C) \\ \end{align} $\text{Note: N/A entries are not included in the calculation.}$

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Problem 527

2. The paralympic committee of a sitting volleyball club has indicated that the mean score achieved by the sports' members in the past was 85.9. A group of members believes that recent changes to the sitting volleyball court have led to a change in the mean score achieved by the club's members and decides to investigate this belief. A random sample of the scores, $x$ , of 100 club members was taken and is summarized by $\sum x=8350 \quad \text { and } \quad \sum(x-\bar{x})^{2}=15321$ where $\bar{x}$ denotes the sample mean. Test, at the $5 \%$ level of significance, the group's belief that the mean score of 85.9 has changed.

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Problem 528

Part 1 of 4 score: $11.11 \%, 1$ of 9 points Points: 0 of 1 Save
Ten people went on a diet for a month. The weight losses experienced (in pounds) are given below. The negative weight loss is a weight gain. Test the hypothesis that the mean weight loss was more than 0 , using a significance level of 0.05 . Assume the population distribution is Normal. $4,8,9,0,3,5,7,3,1 \text {, and }-1$
Determine the null and altemative hypotheses. Choose the correct answer below. A. $\mathrm{H}_{0}: \mu>0$ B. $H_{0}: \mu<0$ C. $H_{0}: \mu=0$
$\mathrm{H}_{\mathrm{a}}: \mu \leq 0$ $H_{a}: \mu \geq 0$ $H_{a}: \mu \neq 0$ D. $H_{0}: \mu=0$ E. $H_{0}: \mu \neq 0$ $H_{a}: \mu>0$ $H_{a}: \mu=0$ F. $H_{0}: \mu=0$ $\mathrm{H}_{\mathrm{a}}: \mu<0$

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Problem 529

A random sample of 10 independent healthy people showed the body temperatures given below (in degrees Fahrenheit). Test the hypothesis that the population mean is not $98.6^{\circ} \mathrm{F}$ , using a significance level of 0.05 . $\begin{array}{llllllllll} 98.5 & 98.4 & 99.0 & 96.1 & 98.8 & 98.7 & 97.2 & 99.2 & 98.9 & 97.5 \end{array}$ answer below. A. $H_{0}: \mu \neq 98.6$ B. $H_{0}: \mu=98.6$ C. $H_{0}: \mu=98.6$ $H_{a}: \mu=98.6$ $H_{a}: \mu<98.6$ $\mathrm{H}_{\mathrm{a}}: \mu>98.6$ D. $H_{0}: \mu<98.6$ E. $\mathrm{H}_{0}: \mu>98.6$ F. $H_{0}: \mu=98.6$ $H_{a}: \mu=98.6$ $H_{a}: \mu=98.6$ $H_{a}: \mu \neq 98.6$
Find the test statistic. $\mathrm{t}=$ $\square$ (Round to two decimal places as needed.) Find the $p$ -value. p -value $=$ $\square$ (Round to three decimal places as needed.)

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Problem 530

1
The weights of four randomly and independently selected bags of tomatoes labeled 5 pounds were found to be 5.2,4.9,5.2, and 5. Assume Normality. a. Using a two-sided alternative hypothesis, should you be able to reject the hypothesis that the population mean is 5pounds using a significance level of 0.05 Why or why not? The confidence interval is reported here: I am 95\%onfident the population mean is between 4.8and 5.3pounds. b. Now test the hypothesis that the population mean is not 5 pounds. Use a significance level of 0.05 . a. Choose the correct answer below. A. Do not reject the hypothesis, because the interval contains the proposed riean. B. Do not reject the hypothesis, because the interval does not contain the proposed mean. C. There is insufficient information to determine if the hypothesis should be rejected. D. Reject the hypothesis, because the interval contains the proposed mean. E. Reject the hypothesis, because the interval does not

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Problem 531

The weights of four randomly and independently selected bags of tomatoes labeled 5 pounds were found to be $5.2,4.9,5.2$ , and 5. 맘 Assume Normality. a. Using a two-sided alternative hypothesis, should you be able to reject the hypothesis that the population mean is 5pounds using a significance level of 0.05 Why or why not? The confidence interval is reported here: I am 95\%onfident the population mean is between 4.8and 5.3pounds. b. Now test the hypothesis that the population mean is not 5 pounds. Use a significance level of 0.05 . b. Determine the null and alternative hypotheses. Choose the correct answer below. A. $\mathrm{H}_{0}: \mu=5$ B. $H_{0}: \mu=5$ C. $\mathrm{H}_{0}: \mu>5$ $H_{a}: \mu<5$ $H_{a}: \mu>5$ $H_{a}: \mu \leq 5$ D. $\begin{array}{l} H_{0}: \mu \neq 5 \\ H_{a}: \mu=5 \end{array}$ E. $\begin{array}{l} H_{0}: \mu=5 \\ H_{a}: \mu \neq 5 \end{array}$ F. $\mathrm{H}_{0}: \mu<5$ $H_{a}: \mu \geq 5$
Find the test statistic. $\mathrm{t}=$ $\square$ (Round to two decimal places as needed.)

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Problem 532

1
In Country A, the population mean height for 3-year-old boys is 39 inches. Suppose a random sample of 153 -year-old boys from Country B showed a sample mean of 38.7 inches with a standard deviation of 4 inches. The boys were independently sampled. Assume that heights are Normally distributed in the population. Complete parts a through c below. a. Determine whether the population mean for Country B boys is significantly different from the Country A mean. Use a significance level of 0.05 .
Which of the following correctly states $\mathrm{H}_{0}$ and $\mathrm{H}_{a}$ ? A. $\begin{array}{l}H_{0}: \mu=39 \\ H_{0}: \mu \neq 39\end{array}$ $H_{0}: \mu \geq 39$ c. $H_{0}: \mu=39$ B. $H_{a}: \mu<39$ . $H_{a}: \mu<39$
$H_{0}: \mu>39$ D. $H_{a}: \mu \leq 39$ $H_{0}: \mu \neq 39$ F. $\begin{array}{l}H_{0}: \mu=39 \\ H_{a}: \mu>39\end{array}$

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Problem 533

$\text{Consider ion 5. How many attractive electrostatic interactions are shown for it? How many repulsive interactions are shown for it? Is the sum of the attractive interactions larger or smaller than the sum of the repulsive interactions? Complete the sentences to explain your answer.}$
$\begin{array}{c} \text{Match the items in the left column to the appropriate blanks in the sentences on the right.} \\ \text{Reset} \\ \text{Help} \\ \square \\ \square \\ \square \\ \square \\ \square \\ \square \\ \text{larger than} \\ \text{smaller than} \\ \text{about the same as} \\ \end{array}$
$\begin{array}{l} \text{Ion 5 has } \square \text{ attractive electrostatic interactions shown for it.} \\ \text{Ion 5 has } \square \text{ repulsive interactions shown for it.} \\ \text{The sum of the attractive interactions (first sentence) is } \square \text{ the sum of the repulsive interactions (second sentence).} \\ \end{array}$

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Problem 534

The following information was obtained when carrying out an experiment to determine the Enthalpyof neutralization $(\Delta \mathrm{H})$ reaction between HCl and NaOH . 100 mL of 2.00 M HCl solution was added to 95.00 mL of 2.00 M solution of NaOH . The final temperature reached was $35.40^{\circ} \mathrm{C}$ and the initial temperature at mixing was $22.15^{\circ} \mathrm{C}$ . The density of the reaction mixture was $1.04 \mathrm{~g} / \mathrm{mL}$ and the specific heat capacity was $3.89 \mathrm{~J} / \mathrm{g}-{ }^{\circ} \mathrm{C}$ . What is the temperature change observed during the reaction? (A) $13.25^{\circ} \mathrm{C}$ (B) $-13.25^{\circ} \mathrm{C}$ (C) $54.55^{\circ} \mathrm{C}$ (D) $5.67^{\circ} \mathrm{C}$

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Problem 535

During the first half of a basketball game, a team made $60 \%$ of their 30 field goal attempts. During the second half, they scored on only $30 \%$ of 40 attempts from the field. What was their field goal shooting percentage for the entire game?
The team's field goal shooting percentage for the entire game was $\square$ \%. (Round to the nearest whole number as needed.)

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Problem 536

In a given population of men and women, $30 \%$ of the men are married and $40 \%$ of the women are married. What percentage of the adult population is married? Assume that, in this particular population, the number of married men is the same as the number of married women.
Of the adult population, $\square$ $\%$ is married. Assume that the number of married men is equal to the number of married women. (Round to two decimal places as needed.)

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Problem 537

Save \& Exit Certity Lesson: 10.1 Introduction to Probability
Question 7 of 16, Step 1 of 1 5/16 Correct JAQUELINE HERNANDEZ
A sample of 400 adults found that 94 do not like cold weather. However, 108 of those studied said that they had interest in taking skiing lessons. Based on this sample, if an adult is chosen at random, what is the probability that he or she has no desire to take skiing lessons? Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.

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Problem 538

The number of ants per acre in the forest is normally distributed with mean 42,000 and standard deviation 12,404 . Let $X=$ number of ants in a randomly selected acre of the forest. Round all answers to 4 decimal places where possible. a. What is the distribution of X ? $\mathrm{X} \sim \mathrm{N}($ $\square$ , $\square$ ) b. Find the probability that a randomly selected acre in the forest has fewer than 52,236 ants. $\square$ c. Find the probability that a randomly selected acre has between 46,025 and 60,884 ants. $\square$ d. Find the first quartile. $\square$ ants (round your answer to a whole number)

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Problem 539

A recent survey showed that 93 full-time employees out of a sample of 400 did not use all of their vacation days last year. However, 118 of those studied expressed a desire for more vacation time. Based on this sample, if a full-time employee is chosen at random, what is the probability that he or she is content with the vacation allowance? Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
Answer Keypac Keyboard Shortcı

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Problem 540

The mean height of an adult giraffe is 19 feet. Suppose that the distribution is normally distributed with standard deviation 1 feet. Let $X$ be the height of a randomly selected adult giraffe. Round all answers to 4 decimal places where possible. a. What is the distribution of X ? $\mathrm{X} \sim \mathrm{N}($ $\square$ , b. What is the median giraffe height? $\square$ ft . c. What is the Z-score for a giraffe that is 20.5 foot tall? $\square$ d. What is the probability that a randomly selected giraffe will be shorter than 18.4 feet tall? $\square$ e. What is the probability that a randomly selected giraffe will be between 18 and 18.5 feet tall? $\square$ f. The 70th percentile for the height of giraffes is $\square$ ft.

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Problem 541

registration records show that households in Elmville have 0 to 5 pets. Suppose that a household in Elmville is randomly selected. Let $X$ be the number of istered pets for that household. Here is the probability distribution of $X$ . \begin{tabular}{|c|c|c|c|c|c|c|} \hline alue $\boldsymbol{x}$ of $\boldsymbol{X}$ & 0 & 1 & 2 & 3 & 4 & 5 \\ \hline $\boldsymbol{P}(X=x)$ & 0.13 & 0.22 & 0.23 & 0.18 & 0.14 & 0.10 \\ \hline \end{tabular} or parts (a) and (b) below, find the probability that the randomly selected household has the number of pets described. (a) Less than 3: $\square$ (b) No less than 3: $\square$ Save For Later Submit Ass

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Problem 542

[2/2 Points] DETAILS MY NOTES OSAPPHYSPREP2016 2.AP.006. PREVIOUS ANSWERS ASK YOUR
A group of students is attempting to determine the average acceleration of a marble released from the top of a long ramp. Below is a set of data representing the marble's position with respect to time. \begin{tabular}{|l|l|} \hline Position (cm) & Time $(\mathrm{s})$ \\ \hline 0.0 & 0.0 \\ \hline 0.4 & 0.5 \\ \hline 1.7 & 1.0 \\ \hline 3.5 & 1.5 \\ \hline 6.2 & 2.0 \\ \hline 9.2 & 2.5 \\ \hline 13.4 & 3.0 \\ \hline \end{tabular}
Use the data table above to construct a graph determining the acceleration of the marble. Select a set of data points from the table and plot those points on the graph. Label the axes and indicate the scale fo through your data points. (Select the graph which would best help you determine the marble's acceleration.)
Using the best-fit line, determine the value of the marble's acceleration (in $\mathrm{cm} / \mathrm{s}^{2}$ ). 3.04 $\mathrm{cm} / \mathrm{s}^{2}$

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Problem 543

The following table describes the contents of a bag that contains red, green, blue, pink, and white marbles. \begin{tabular}{|c|c|} \hline Color & Number of Marbles \\ \hline Red & 12 \\ \hline Green & 6 \\ \hline Blue & 10 \\ \hline Pink & 9 \\ \hline White & 30 \\ \hline \end{tabular}
If you select a single marble out of the bag, what is the probability that it is a color other than white or blue? Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.

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Problem 544

The following table lists the ages and number of players per age group that are on a hockey team. Let $A=\{$ hockey players who are 12 years old $\}$ . How many players are in the complement of $A$ ? \begin{tabular}{|c|c|} \hline \multicolumn{2}{|c|}{\begin{tabular}{c} Ages of Players on \\ Hockey Team \end{tabular}} \\ \hline Age & Number of Players \\ \hline 9 & 2 \\ \hline 10 & 5 \\ \hline 11 & 9 \\ \hline 12 & 3 \\ \hline \end{tabular}

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Problem 545

The table shows the number of degrees the temperature increased or decreased over four days. \begin{tabular}{|c|c|} \hline \multicolumn{2}{|c|}{ Temperature } \\ \hline Day & Temperature Change \\ \hline Tuesday & $-9^{\circ}$ \\ \hline Wednesday & $+6^{\circ}$ \\ \hline Thursday & $+10^{\circ}$ \\ \hline Friday & $-12^{\circ}$ \\ \hline \hline \end{tabular}
On which day did the temperature change have the greatest magnitude? Tuesday Wednesday Thursday Friday

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Problem 546

Which day was the weather forecast most accurate? \begin{tabular}{|c|c|} \hline \multicolumn{2}{|c|}{ Forecast vs Actual Temperature } \\ \hline Day & \begin{tabular}{c} Degrees above $(+)$ or \\ below $(-)$ forecast \end{tabular} \\ \hline Monday & +4 \\ \hline Tuesday & -6 \\ \hline Wednesday & +7 \\ \hline Thursday & -2 \\ \hline \hline \end{tabular} Monday Tuesday Wednesday Thursday

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Problem 547

4 5 6 7 8 9 10
Oscar bought shares in four different stocks. The chart below shows the changes in the stocks' values over the past week. Which stock is closest to its purchase price? \begin{tabular}{|c|c|} \hline \multicolumn{2}{|c|}{ Oscar's Stocks } \\ \hline Stock & Change \\ \hline ABC Toys & $-\$ 3$ \\ \hline Golden Grains & $+\$ 4$ \\ \hline Fast Cars & $-\$ 8$ \\ \hline XYZ Clothing & $+\$ 1$ \\ \hline \hline \end{tabular} ABC Toys Golden Grains Fast Cars XYZ Clothing

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Problem 548

A coin flip determines who gets the ball first at the beginning of a football game, with the visiting team calling heads or tails. The captain of one particular team always calls heads. In the first four games as visitor of a season, find the probability that his team (a) Wins the toss one time. (b) Loses the toss four times. (c) Wins the toss more than once. (d) Loses the toss no more than three times. (e) Loses the toss at least twice.
Write your answers in exact, simplified form.
Part 1 of 5 (a) The probability that the team wins the toss one time is 0.25 .
Part 2 of 5 (b) The probability that the team loses the toss all four times is $\frac{1}{16}$ .
Part 3 of 5 (c) The probability that the team wins the toss more than once is $\square$ .
Part 4 of 5 (d) The probability that the team loses the toss no more than three times is $\frac{15}{16}$ .
Part 5 of 5 (e) The probability that the team loses the toss at least twice is $\frac{11}{16}$ .

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Problem 549

The following table shows fuel consumption in billions of gallons of all vehicles in the U.S. for years since 1990. \begin{tabular}{|c|c|} \hline Year & Fuel Use \\ \hline 0 & 130.8 \\ \hline 3 & 137.3 \\ \hline 6 & 147.4 \\ \hline 9 & 161.4 \\ \hline 12 & 168.7 \\ \hline 15 & 174.8 \\ \hline 18 & 170.8 \\ \hline \end{tabular}
Let $F(t)$ be the fuel consumption in billions of gallons in $t$ years since 1990. A quadratic model for the data is $F(t)=-0.114 t^{2}+4.62 t+127.598$ .
Use the above scatter plot to decide whether the quadratic model fits the data well. The function is a good model for the data. The function is not a good model for the data Estimate the fuel consumption in the U. S. in 2010. $\square$ billions of gallons.
Use the model to predict the year in which U.S. fuel consumption will peak. $\square$

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Problem 550

Use the following table to find the probability that a randomly chosen member of the Student Government Board is a freshman or lives in on-campus housing. Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth. \begin{tabular}{|c|c|c|} \hline \multicolumn{3}{|c|}{ Students on the Student Government Board } \\ \hline Classification & On-Campus Housing & Off-Campus Housing \\ \hline Freshman & 3 & 0 \\ \hline Sophomore & 2 & 3 \\ \hline Junior & 1 & 1 \\ \hline Senior & 3 & 2 \\ \hline Graduate Student & 1 & 1 \\ \hline \end{tabular}

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Problem 551

To choose the order of bands for the finals of a Battle of the Bands competition, Freddy puts a penny, a nickel, a dime, a quarter, and a half-dollar into five separate envelopes and has one band choose an envelope. The second band then chooses from the remaining envelopes. Draw a tree diagram to determine the sample space and find the probabilities for the selections of the two bands in the finals. Express probabilities as simplified fractions.
Part 1 of 6 (a) The sample space contains 20 outcomes.
Part 2 of 6 (b) Find the probability that the amount of the first coin is more than the amount of the second coin.
The probability that the amount of the first coin is more than the amount of the second coin is $\frac{1}{2}$ .
Part: $2 / 6$
Part 3 of 6 (c) Find the probability that neither coin is a nickel.
The probability that neither coin is a nickel is $\square$

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Problem 552

At your local carnival, there is a game where 40 rubber duckies are floating in a kiddie tub, and they each have their bottoms painted one of three colors. 7 are painted pink, 15 are painted blue, and 18 are painted purple. If the player selects a duck with a pink bottom, they receive three pieces of candy. If they select blue, they receive two pieces of candy. And if they select purple, they receive one piece of candy. If the game is played 78 times, what are the minimum and maximum amounts of candy that could be handed out?
Answer Keypad Keyboard Shortcut $\square$
Activate Windows Go to Settings to activate Win

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Problem 553

Save \& Exit Certify Lesson: 10.6 Expected Value JAQUELINE HERNANDEZ Question 3 of 15, Step 1 of 1 2/15 Correct 2
At your local carnival, there is a game where 40 rubber duckies are floating in a kiddie tub, and they each have their bottoms painted one of three colors. 5 are painted pink, 17 are painted blue, and 18 are painted purple. If the player selects a duck with a pink bottom, they receive three pieces of candy. If they select blue, they receive two pieces of candy. And if they select purple, they receive one piece of candy. If the game is played 75 times, what are the minimum and maximum amounts of candy that could be handed out?

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Problem 554

A shoe company conducts a survey to determine the expected value of online sales for their new line of shoes coming out next fall. Based on past years, they have observed the following data on the probability of selling different types of shoes in the new line. The company expects that 3493 people will visit the website for their new line on launch day. Note that some of the online shoppers will not make a purchase. \begin{tabular}{|c|c|c|} \hline Shoe type & Price & Probability \\ \hline Sneakers & $\$ 93.99$ & $\frac{3}{25}$ \\ \hline High heels & $\$ 83.25$ & $\frac{1}{20}$ \\ \hline Sandals & $\$ 50.50$ & $\frac{1}{10}$ \\ \hline Loafers & $\$ 70.75$ & $\frac{4}{25}$ \\ \hline \end{tabular}
How much should the company expect its shoppers to spend on the website on launch day? Round your answer to the nearest cent, if necessary.

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Problem 555

A researcher randomly purchases several different kits of a popular building toy. The following table shows the number of pieces in each kit in the sample. Find the range of the data. \begin{tabular}{|c|c|} \hline \multicolumn{2}{|c|}{\begin{tabular}{c} Building \\ Toy Pieces \end{tabular}} \\ \hline 166 & 51 \\ \hline 271 & 356 \\ \hline 356 & 51 \\ \hline 110 & 302 \\ \hline 271 & 115 \\ \hline 176 & 498 \\ \hline \end{tabular}

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Problem 556

Here are some facts about units of volume. \begin{tabular}{|c|c|c|} \hline Unit & Symbol & Fact \\ \hline fluid ounce & fl oz & \\ \hline \end{tabular} \begin{tabular}{ccc} cup & c & $1 \mathrm{c}=8 \mathrm{fl} \mathrm{oz}$ \\ pint & pt & $1 \mathrm{pt}=2 \mathrm{c}$ \\ \hline quart & qt & $1 \mathrm{qt}=2 \mathrm{pt}$ \\ \hline gallon & gal & $1 \mathrm{gal}=4 \mathrm{qt}$ \end{tabular}
Fill in the blanks. $\begin{aligned} 4 \mathrm{pt} & =\llbracket \mathrm{c} \\ 28 \mathrm{qt} & =\square \mathrm{gal} \end{aligned}$

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Problem 557

Find the median of the following data set. Assume the data set is a sample. $38,51,34,40,45,41,53,47,46,33,40,42$
Answer How to enter your answer (opens in new window)

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Problem 558

A teaching assistant collected data from students in one of her classes to investigate whether study time per week (average number of hours) differed between students in the class who planned to go to graduate school and those who did not. Complete parts (a) through (c).
Click the icon to view the data. $s_{1}=8.22$ (Round to the nearest hundredth as needed.) Find the standard deviation for students who did not plan to go to graduate school. $s_{2}=3.35$ (Round to the nearest hundredth as needed.) Interpret these values. A. The sample mean was higher for the students who planned to go to graduate school, but the tir B. The sample mean was lower for the students who planned to go to graduate school, but the tim C. The sample mean was lower for the students who planned to go to graduate school, but the tim D. The sample mean was higher for the students who planned to go to graduate school, but the tir Print
Data table \begin{tabular}{|c|} \hline Fraduate school: $17,7,15,10,5,5,2,3,12,16,15,35,8$ , \\ $14,10,19,3,26,15,5,5$ \end{tabular} b. Find the standard error for the difference between the sample means. Interpret.
Find the standard error for the difference between the sample means. $s e=2.08$ (Round to the nearest hundredth as needed.) Interpret this value. A. If further random samples of these sizes were obtained from these populations, the differences between the sample means would vary. The standard deviation of these values for ( $\left.\bar{x}_{1}-\bar{x}_{2}\right)$ would equal about 2.1. B. If further random samples of these sizes were obtained from these populations, the differences between the sample means would not vary. The value of ( $\left.\bar{x}_{1}-\bar{x}_{2}\right)$ would equal about 2.1 . C. If further random samples of these sizes were obtained from these populations, the differences between the sample means would vary. The standard deviation of these values for ( $\left.\bar{x}_{1}-\bar{x}_{2}\right)$ would equal about 4.2 .

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Problem 559

Current Attempt in Progress
The following is a set of hypotheses, some information from one or more samples, and a standard error from a randomization distribution.
Test $H_{0}: p=0.25$ vs $H_{a}: p<0.25$ when the sample has $n=700$ , and $\hat{p}=0.225$ with $S E=0.02$ .
Find the value of the standardized $z$ -test statistic.
Round your answer to two decimal places. $z=$ i

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Problem 560

If $X$ represents a random variable coming from a normal distribution with mean 3 and if $P(X>4.1)=0.23$ , then $P(3<X<4.1)=0.27$ . True False

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Problem 561

MORE BENEFITS OF EATING ORGANIC
Using specific data, we find a significant difference in the proportion of fruit flies surviving after 13 days between those eating organic potatoes and those eating conventional (not organic) potatoes. This exercise asks you to conduct a hypothesis test using additional data. In this case, we are testing $\begin{array}{l} H_{0}: p_{o}=p_{c} \\ H_{a}: p_{o}>p_{c} \end{array}$ where $p_{o}$ and $p_{c}$ represent the proportion of fruit flies alive at the end of the given time frame of those eating organic food and those eating conventional food, respectively. Use a $5 \%$ significance level.
Effect of Organic Soybeans After 5 Days
After 5 days, the proportion of fruit flies eating organic soybeans still alive is 0.9 , while the proportion still alive eating conventional soybeans is 0.84. The standard error for the differeffee in proportions is 0.022 .
What is the value of the test statistic?
Round your answer to two decimal places. $\square$ What is the $p$ -value?
Round your answer to three decimal places. $p \text {-value = }$ $\square$
What is the conclusion?

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Problem 562

20. (C) MP. 3 Critique Reasoning There are 50 communities in Kalb County. Each community has about the same number of people. Marty estimates there are about 300 people living in each community. Is his estimate reasonable? Justify your answer.
Population of Counties

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Problem 563

Use $n=6$ and $p=0.25$ to complete parts (a) through (d) below. \begin{tabular}{l|l|} \hline 1 & 0.3560 \\ \hline 2 & 0.2966 \\ \hline 3 & 0.1318 \\ \hline 4 & 0.0330 \\ \hline 5 & 0.0044 \\ \hline 6 & 0.0002 \\ \hline \end{tabular} (Round to four decimal places as needed.) (b) Compute the mean and standard deviation of the random variable using $\mu_{X}=\sum[x \cdot P(x)]$ and $\sigma_{x}=\sqrt{\sum\left[x^{2} \cdot P(x)\right]-\mu_{x}^{2}}$ $\mu_{X}=$ $\square$ (Round to two decimal places as needed.) $\sigma_{X}=$ $\square$ (Round to two decimal places as needed.) (c) Compute the mean and standard deviation, using $\mu_{X}=n p$ and $\sigma_{X}=\sqrt{n p(1-p)}$ . $\mu_{X}=$ $\square$ (Round to two decimal places as needed.) $\sigma_{x}=$ $\square$ (Round to two decimal places as needed.)

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Problem 564

Eat your cereal: Boxes of cereal are labeled as containing 14 ounces. Following are the weights, in ounces, of a sample of 12 boxes. It is reasonable to assume that the population is approximately normal. \begin{tabular}{llllll} \hline 13.01 & 14.96 & 13.10 & 13.11 & 13.09 & 13.01 \\ 13.14 & 14.96 & 13.04 & 13.03 & 13.10 & 13.11 \\ \hline \end{tabular} Send data to Excel
Part: $0 / 2$
Part 1 of 2 (a) Construct a $90 \%$ confidence interval for the mean weight. Round the answers to at least three decimal places.
A $90 \%$ confidence interval for the mean weight is $12.818^{\otimes}<\mu<13.458{ }^{\otimes}$ .

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Problem 565

Match basketball players with respect to general athletic ability in order to test different kinds of athletic shoes. Independent Samples t-Test Related Samples t-Test

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Problem 566

According to flightstats.com, American Airlines flights from Dallas to Chicago are on time $80 \%$ of the time. Suppose 25 flights are randomly selected, and the number of on-time flights is recorded. (a) Explain why this is a binomial experiment. (b) Determine the values of $n$ and $p$ . (c) Find and interpret the probability that exactly 15 flights are on time. (d) Find and interpret the probability that fewer than 15 flights are on time. (e) Find and interpret the probability that at least 15 flights are on time. (f) Find and interpret the probability that between 13 and 15 flights, inclusive, are on time. (c) Using the binomial distribution, the probability that exactly 15 flights are on time is $\square$ (Round to four decimal places as needed.) Interpret the probability. In 100 trials of this experiment, it is expected that about (Round to the nearest whole number as needed.) $\square$ will result in exactly 15 flights being on time. (d) Using the binomial distribution, the probability that fewer than 15 flights are on time is (Round to four decimal places as needed.) $\square$ Interpret the probability. In 100 trials of this experiment, it is expected that about $\square$ will result in fewer than 15 flights being on time. (Round to the nearest whole number as needed.)

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Problem 567

eans [501 2cola Points: 0.0 l 1 Save
A formal hypothesis test is to be conducted to test the claim that the wait times at the Space Mountain ride in Wat Disney World have a mean equal to 47 minutes. Complete parts (a) through (d). a. What is the null hypothesis, and how is it denoted? $\mathrm{H}_{0}$ $\mu$ $\square$ $=$ 47 minute(s) $\square$ (Type an integer or a decimal. Do not round.) b. What is the alternative hypothesis, and how is it denoted? $\square$ $\mathrm{H}_{\mathrm{pa}}$ $\square$ $=$ $\square$ minute(s) ur or a decimal. Do not round.)

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Problem 568

1. Statistical Literacy List three methods of assigning probabilities.
2. Statistical Literacy Suppose a weather app says that the probability of rain today is $30 \%$ . What is the complement of the event "rain today"? What is the probability of the complement? (3.) Statistical Literacy What is the probability of (a) an event $A$ that is certain to occur? (b) an event $B$ that is impossible?
4. Statistical Literacy What is the law of large numbers? If you were using the relative frequency of an event to estimate the probability of the event, would it be better to use 100 trials or 500 trials? Explain.

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Problem 569

The mean GPA of all 7000 students at a college is 2.08 . A sample of 200 GPAs from this school has a mean of 2.66 . Which number is $\mu$ and which is $\bar{x}$ ?
Choose the correct answer below. A. The statistic is $\bar{x}=2.08$ , and the parameter is $\mu=2.66$ . B. The statistic is $\mu=2.08$ , and the parameter is $\bar{x}=2.66$ . C. The population mean is $\mu=2.08$ , and the sample mean is $\bar{x}=2.66$ . D. The population mean is $\bar{x}=2.08$ , and the sample mean is $\mu=2.66$ .

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Problem 570

14. Critical Thinking (a) Explain why -0.41 cannot be the probability of some event. (b) Explain why 1.21 cannot be the probability of some event. (c) Explain why $120 \%$ cannot be the probability of some event. (d) Can the number 0.56 be the probability of an event? Explain.
15. Probability Estimate: Wiggle Your Ears Can you wiggle your ears?
Use the students in your statistics class (or a group of friends) to estimate the percentage of people who can wiggle their ears. How can your result be thought of as an estimate for the probability that a person chosen at random can wiggle his or her ears? Comment: National statistics indicate that about $13 \%$ of Americans can wiggle their ears (Source: Bernice Kanner, Are You Normal?, St. Martin's Press, New York).
16. Probability Estimate: Raise One Eyebrow Can you raise one eyebrow at a time? Use the students in your statistics class (or a group of friends) to estimate the percentage of people who can raise one eyebrow at a time. How can your result be thought of as an estimate for the probability that a person chosen at random can raise one eyebrow at a time? Comment: National statistics indicate that about $30 \%$ of Americans can raise one eyebrow at a time (see source in Problem 15).
17. Myers-Briggs: Personality Types Isabel Briggs Myers was a pioneer in the study of personality types. The personality types are broadly defined according to four main preferences. Do married couples choose similar or different personality types in their mates? The following data give an indication (Source: I. B. Myers and M. H. McCaulley, A Guide to the Development and Use of the Myers-Briggs Type Indicators).
Similarities and Differences in a Random Sample of 375 Married Couples \begin{tabular}{lc} \hline Number of Similar Preferences & Number of Married Couples \\ \hline All four & 34 \\ Three & 131 \\ Two & 124 \\ One & 71 \\ None & 15 \\ \hline \end{tabular}
Suppose that a married couple is selected at random. (a) Use the data to estimate the probability that they will have $0,1,2,3$ , or 4 personality preferences in common. (b) Do the probabilities add up to 1? Why should they? What is the sample space in this problem?
18. General: Roll a Die (a) If you roll a single fair die and count the number of dots on top, what is the sample space of all possible outcomes? Are the outcomes equally likely? (b) Assign probabilities to the outcomes of the sample space of part (a). Do the probabilities add up to 1 ? Should they add up to 1? Explain. (c) What is the probability of getting a number less than 5 on a single throw? (d) What is the probability of getting 5 or 6 on a single throw?

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Problem 571

Left-Handed Lawyers Approximately $10 \%$ of Americans are left-handed (we will treat this as a known population parameter). A study on the relationship between handedness and profession found that in a random sample of 105 lawyers, 16 of them were lefthanded. ${ }^{1}$ Test the hypothesis that the proportion of left-handed lawyers differs from the proportion of left-handed Americans. ${ }^{1}$ Schachter, S. and Ransil, B., "Handedness Distributions in Nine Professional Groups," Perceptual and Motor Skills, 1996; 82: 51-63.
Part 1
Clearly state the null and alternative hypotheses. Let $p$ be the proportion of left-handed lawyers. eTextbook and Media Save for Later Attempts: 0 of 5 used Submit Answer
Part 2
Calculate the test statistic and $p$ -value. Round your answer for the test statistic to two decimal places, and your answer for the $p$ -value to three decimal places. test statistic $=$ $\square$ i $\square$ $p$ -value $=$ eTextbook and Media

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Problem 572

Agriculture: Cotton A botanist has developed a new hybrid cotton plant that can withstand insects better than other cotton plants. However, there is some concern about the germination of seeds from the new plant. To estimate the probability that a seed from the new plant will germinate, a random sample of 3000 seeds was planted in warm, moist soil. Of these seeds, 2430 germinated. (a) Use relative frequencies to estimate the probability that a seed will germi. nate. What is your estimate? (b) Use relative frequencies to estimate the probability that a seed will not germinate. What is your estimate? (c) Either a seed germinates or it does not. What is the sample space in this problem? Do the probabilities assigned to the sample space add up to 1 ? Should they add up to 1? Explain. (d) Are the outcomes in the sample space of part (c) equally likely?

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Problem 573

8) An office at the college reports there is a $70 \%$ chance of a student passing a certain professor's prealgebra class. Represent a student passing as a success. a) In a class of 25 students use the Binomial Probability Formula to find the probability that if 5 students are selected that exactly 3 pass. b) Determine the mean and standard deviation using the formulas on p234 of the text.

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Problem 574

Current Attempt in Progress
Consider random samples of size 46 drawn from population A with proportion 0.34 and random samples of size 36 drawn from population $B$ with proportion 0.28 .
Part 1 (a) Find the standard error of the distribution of differences in sample proportions, $\hat{p}_{A}-\hat{p}_{B}$
Round your answer for the standard error to three decimal places. standard error $=$ $\square$ eTextbook and Media $\square$ Save for Later Attempts: 0 of 5 used Submit Answer
Part 2

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Problem 575

12. Critical Thinking Consider the experiment of tossing a fair coin three times, For each coin, the possible outcomes are heads or tails. (a) List the equally likely events of the sample space for the three tosses. (b) What is the probability that all three coins come up heads? Notice that the complement of the event "three heads" is "at least one tail." Use this information to compute the probability that there will be at least one tail.
13. Critical Thinking On a single toss of a fair coin, the probability of heads is 0.5 and the probability of tails is 0.5 . If you toss a coin twice and get heads on the first toss, are you guaranteed to get tails on the second toss? Explain.

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Problem 576

\text{At 0.905 atm and 400 K, which of the following gases would NOT have the same molar volume as the others?} \\ \text{He, O}_2, \text{CO}_2 \\

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Problem 577

Suppose 250 subjects are treated with a drug that is used to treat pain and 53 of them developed nausea. Use a 0.05 significance level to test the claim that more than $20 \%$ of users develop nausea. $H_{1}: p<0.20$ B. $H_{0}: p=0.20$ $H_{1}: p>0.20$ C. $H_{0}: p>0.20$ $H_{1}: p=0.20$ D. $H_{0}: p=0.20$ $H_{1}: p \neq 0.20$
Identify the test statistic for this hypothesis test. The test statistic for this hypothesis test is 0.47 . (Round to two decimal places as needed.) Identify the P-value for this hypothesis test. The P-value for this hypothesis test is $\square$ (Round to three decimal places as needed.)

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Problem 578

Part 2 of 4 Points: 0.6 of 1 Save e data table contains waiting times of customers at a bank, where customers enter a single waiting line that feeds three teller windows. Test the claim that the standard deviation waiting times is less than 1.7 minutes, which is the standard deviation of waiting times at the same bank when separate waiting lines are used at each teller window. Use a nificance level of 0.01 . Assume that the sample is a simple random sample selected from a normally distributed population. Complete parts (a) through (d) below.
Click on the icon to view the data. dentify the null and alternative hypotheses. Choose the correct answer below. A. $H_{0}: \sigma=1.7$ minutes $H_{A}: \sigma<1.7$ minutes C. $H_{0}: \sigma<1.7$ minutes $\mathrm{H}_{\mathrm{A}}: \sigma=1.7$ minutes
Oompute the test statistic. $\square$ und to two decimal places as needed.) Customer Waiting Times \begin{tabular}{|c|c|c|c|} \hline \multicolumn{4}{|c|}{\begin{tabular}{c} Customer Waiting Times \\ (in minutes) \end{tabular}} \\ \hline 7.2 & 7.4 & 8.8 & 7.7 \\ \hline 6.7 & 7.8 & 6.8 & 7.1 \\ \hline 6.1 & 7.5 & 8.5 & 7.6 \\ \hline 7.1 & 6.9 & 5.4 & 6.9 \\ \hline 8.6 & 8.5 & 9.3 & 7.9 \\ \hline 7.3 & 8.4 & 6.9 & 7.4 \\ \hline 6.2 & 6.2 & 7.4 & 6.7 \\ \hline 7.3 & 6.3 & 7.1 & 7.9 \\ \hline 7.6 & 9.2 & 6.3 & 6.7 \\ \hline 6.1 & 6.8 & 7.7 & 7.8 \\ \hline 7.6 & 6.5 & 7.5 & 6.9 \\ \hline 8.7 & 6.7 & 7.7 & 6.4 \\ \hline 8.9 & 6.3 & 8.6 & 6.1 \\ \hline 7.5 & 6.4 & 6.2 & 8.5 \\ \hline 6.6 & 7.9 & 6.6 & 7.8 \\ \hline \end{tabular}

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Problem 579

```latex \textbf{Aufgabe 1: Badewanne}
In eine leere Badewanne wird eine gewisse Zeitlang gleichförmig Wasser eingelassen, dann die Wasserzufuhr gestoppt, gleichzeitig der Abfluss geöffnet und nach einer Weile wieder geschlossen. Das Bild oben links zeigt den Verlauf des Vorgangs.
\begin{enumerate} \item[a)] Bestimmen Sie, welche Wassermenge sich nach 2 Minuten in der Badewanne befand! (2 BE) \item[b)] Rekonstruieren Sie, welche Wassermenge insgesamt in dieser Zeit gepumpt wurde. (2 BE) \item[c)] Bestimmen Sie, nach welcher Zeit die Badewanne wieder leer ist! (2 BE) \item[d)] Rekonstruieren Sie auch, welche Wassermenge sich nach 2 Minuten in der Badewanne befand, wenn der Vorgang gemäß dem Bild oben rechts geschieht (die Funktionen lassen sich leicht bestimmen!). (4 BE) \end{enumerate} ```

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Problem 580

```latex \text{The graph represents changes in the house pricing index over 28 years. Rank the investment strategies from least to greatest profit.}

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Problem 581

Answer Submitted: (a) Use the credit card statement to help fill in the table below. Note that there are 31 days in March. Also, a purchase increases the unpaid balanci payment decreases the unpaid balance. \begin{tabular}{|c|c|c|c|c|c|} \hline Date & Transaction & Transaction amount & Unpaid balance & Number of days at that balance & Unpaid $\times$ Number balance ${ }^{x}$ of days \\ \hline March 1 & Beginning balance & \2200.06 & \$2200.06 & 7 days (from March 1 through March 7) & \$15,400.42 \\ \hline March 8 & Payment & \$370.00 & \$1830.06 & 3 days (from March 8 through March 10) & \$5490.18 \\ \hline March 11 & Purchase & \ $35.75$ & \$1865.81 & 10 days (from March 11 through March 20) & \$18658.10 \\ \hline March 21 & Payment & \$800.00 & \$1065.81 & 11 days (from March 21 through March 31) & \$11723.91 \\ \hline \end{tabular}
Total: 31 days Total: $\$ 51272.61$ (b) Find the average daily balance. Write your answer to the nearest cent. $\$ 1653.96$ (c) Suppose the credit card company charges an interest rate of $1.7 \%$ on the average daily balance for March found in part (b). How much interest will be charged? Write your answer to the nearest cent. $\$ 28.12$ (d) What will Ali's beginntig balance be for the month of April (including the interest for March found in part (c))? $\$ 1093.93$

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Problem 582

There is a $50 \%$ chance of having a child that is either a boy or a girl. If a couple has three girls, what is the probability their 4th child will be another girl?

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Problem 583

Question 1 1 pts
A random sample of size 20 drawn from a normal population yielded the following results: $\bar{x}=49.2, s=1.33$ .
In testing: $H_{0}: \mu=50$ versus $H_{1}: \mu \neq 50$ at a 0.01 level of significance, the decision is to: not reject the null hypothesis. reject the null hypothesis.

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Problem 584

Linear Regression Application, Interpolation and Extrapolation Use the data and story to answer the following questions The table below shows the number of state-registered automatic weapons and the murder rate for several Northwestern states. \begin{tabular}{|r|r|r|r|r|r|r|r|r|} \hline $x$ & 11.7 & 8.3 & 7.1 & 3.8 & 2.8 & 2.4 & 2.4 & 0.9 \\ \hline $y$ & 14.3 & 11 & 10.2 & 7 & 6.6 & 6.2 & 6.2 & 4.5 \\ \hline \end{tabular} $x=$ thousands of automatic weapons $y=$ murders per 100,000 residents Use your calculator to determine the equation of the regression line. (Round to 2 decimal places) Determine the regression equation in $\mathrm{y}=\mathrm{ax}+\mathrm{b}$ form and write it below. A) How many murders per 100,000 residents can be expected in a state with 8.2 thousand automatic weapons?
Answer = $\square$ Round to 3 decimal places. B) How many murders per 100,000 residents can be expected in a state with 8.9 thousand automatic weapons?
Answer = $\square$ Round to 3 decimal places.

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Problem 585

``` \ Linear Regression Application, Interpolation and Extrapolation Use the data and story to answer the following questions ```
The table below shows the number of state-registered automatic weapons and the murder rate for several Northwestern states. \begin{tabular}{|r|r|r|r|r|r|r|r|r|} \hline $x$ & 11.7 & 8.3 & 7.1 & 3.8 & 2.8 & 2.4 & 2.4 & 0.9 \\ \hline $y$ & 14.3 & 11 & 10.2 & 7 & 6.6 & 6.2 & 6.2 & 4.5 \\ \hline \end{tabular} $x=$ thousands of automatic weapons $y=$ murders per 100,000 residents Use your calculator to determine the equation of the regression line. (Round to 2 decimal places) Determine the regression equation in $y=a x+b$ form and write it below. $\square$ A) How many murders per 100,000 residents can be expected in a state with 8.2 thousand automatic weapons?
Answer = $\square$ This is not a decimal or integer value. Round to 3 decimal places. B) How many murders per 100,000 residents can be expected in a state with 8.9 thousand automatic weapons?
Answer = $\square$ Round to 3 decimal places.

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Problem 586

7. A company advertises on a website. A worker tracked the number of visits to the website and the number of clicks on the advertisement. The table shows the data for several days. A linear function can be used to model the data.
Website Advertisement \begin{tabular}{|c|c|} \hline \begin{tabular}{c} Number of Visits \\ to Website, $x$ \end{tabular} & \begin{tabular}{c} Number of Clicks \\ on Advertisement, $y$ \end{tabular} \\ \hline 153 & 14 \\ \hline 629 & 38 \\ \hline 471 & 30 \\ \hline 914 & 53 \\ \hline 307 & 21 \\ \hline 1,045 & $60^{5}$ \\ \hline 510 & 32 \\ \hline 1,106 & 63 \\ \hline \end{tabular} 105 Add note Question Guide Exi $\Delta$ p ?
Based on the table, what is the best prediction of the number of clicks on the advertisement if 1,500 people visit the website?

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Problem 587

Classify the following scenario as a meta-analysis or a case study.
A town council studies ten newspaper articles about crime prevention.
Answer 2 Points Meta-Analysis Case Study

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Problem 588

5. Which is most likely the correlation coefficient for the line of best fit for the data shown in the scatter plot? Circle the correct answer (a) -0.977 (b) 0.273 (c) -0.296 (d) 0.961

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Problem 589

3. A regression was run to determine if there is a relationship between the diameter ( $x$ ,ininches) of a silver maple silver and the tree's age ( $y$ ,ininches). The results of the regression are below. Use this to predict the age of a silver maple tree with diameter 22 inches. Round your answer to three decimal places. $\begin{array}{l} y=a x+b \\ a=3.679 \\ b=-0.54 \\ r=0.967 \end{array}$ age of tree: $\qquad$ $y=80.936$

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Problem 590

Calculate the Capital Intensity Ratio given the following information: Asset $=1.5 \mathrm{M}$ Sales $=3 \mathrm{M}$ Income $=0.5 \mathrm{M}$ CapEx = 1 M Debt $=.5 \mathrm{M}$ Equity = 1 M

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Problem 591

Emilio took a random sample of $n=12$ giant Pacific octopi and tracked them to calculate their mean lifespan. Their lifespans were roughly symmetric with a mean of $\bar{x}=4$ years and a standard deviation of $s_{x}=0.5$ years. He wants to use this data to construct a $t$ interval for the mean lifespan o! this type of octopus with $90 \%$ confidence.
What critical value $t^{*}$ should Emilio use?

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Problem 592

Dance Company Students The number of students who belong to the dance company at each of several randomly selected small universities is shown below. Round sample statistics and final answers to at least one decimal place. \begin{tabular}{llllllll} 27 & 21 & 47 & 21 & 32 & 32 & 35 & 29 \\ 35 & 26 & 35 & 30 & 21 & 21 & 32 & 25 \end{tabular}
Send data to Excel
Estimate the true population mean size of a university dance company with $95 \%$ confidence. Assume the variable is normally distributed.

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Problem 593

Dance Company Students The number of students who belong to the dance company at each of several randomly selected small universities is shown below. Round sample statistics and final answers to at least one decimal place. \begin{tabular}{llllllll} 27 & 21 & 47 & 21 & 32 & 32 & 35 & 29 \\ 35 & 26 & 35 & 30 & 21 & 21 & 32 & 25 \end{tabular}
Send data to Excel
Estimate the true population mean size of a university dance company with $95 \%$ confidence. Assume the variable is normally distributed.

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Problem 594

Review for Exam 2
1. A test has a mean of 65 and standard deviation of 20 . Using the normal distribution find a) the percentage of scores between 35 and 90 b) the percentage of scores above 60 c) the percentage of scores below 105 d) the percentage of scores below 58 e) the percentage of scores above 93 f) the percentage of scores between 65 and 90 g) the percentage of scores between 85 and 100
2. The average commuting time for a sample of 500 students is 8.5 minutes with a standard deviation of 1.5 . What is the average commute time for the population? Use a $95 \%$ confidence level.
3. Data from the Gallup poll show that $46 \%$ of a random sample of 1005 adults were in favor of the death penalty for a person convicted of murder. What is the level of support for the death penalty among the adult population of the US? Use a $99 \%$ confidence level.
4. From the 2020 GSS subsample, we find that 995 respondents out of a sample of 1500 believe in some form of life after death. What is your population estimate at the $95 \%$ confidence level and the $99 \%$ confidence level?

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Problem 595

The following data was calculated during a study on refinancing. Use the following information to find the test statistic and critical value(s) at a $5 \%$ level of significance: - A realtor believes the average number of times a mortgage is refinanced is different than 3.6 times. - Sample size $=40$ mortgages - Sample mean $=3.7$ times - From past data, it is known that the population standard deviation is 1.1 times.
Use the curve below to find the test statistic and critical value(s). Select the appropriate test by dragging the point vertically to a right-, left- or two-tailed diagram, then set the sliders. Use the alpha slider to set the significance level. Use the sliders to set the information from the study described above including the sample size, sample mean, population mean and standard deviation.
If entering two critical values as your final answer, use $\pm$ .
Move the dot to choose the appropriate test
Provide your answer below: test statistic $=$ $\square$ critical value(s) $=$ $\square$

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Problem 596

B 100 149 8 Height (feet) 120 100 40 20 After 4.5 seconds, what was the object's height? O A. 80 feet ○ B. 90 feet ○ C. 110 feet O D. 120 feet Height of Object arter Launch 7 2 Time (seconds)

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Problem 597

Gromerlige. Gersuse
The table shows the linear relationship between the balance of a student's savings account and the number of week he has been saving. \begin{tabular}{|c|c|c|c|c|c|c|} \hline Weich - & 0 & 1 & 3 & 6 & 8 & 13 \\ \hline \begin{tabular}{c} Balance \\ (doflars) \end{tabular} & 32 & 39 & 53 & 74 & 88 & 123 \\ \hline \end{tabular} the student saves the same money each week, how much money did the student save after 7 weeks? A. $\$ 75$ B. $\$ 81$ C. $\$ 67$ D. $\$ 86$

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Problem 598

Rachel, a city employee, would like to make the claim that the average amount that residents spend per month on public transit fare is less than $\$ 140$ . Rachel samples 25 city residents and obtains a sample mean of $\$ 125.80$ spent per month on public transit.
At the $5 \%$ significance level, should Rachel reject or fail to reject the null hypothesis given the sample data below? - $H_{0}: \mu=\$ 140$ per month; $H_{a}: \mu<\$ 140$ per month - $\alpha=0.05$ (significance level) - test statistic $=-0.52$
Use the graph below to select the type of test (left-, right-, or two-tailed). Then set the $\alpha$ and the test statistic to determine the $p$ -value. Use the results to determine whether to reject or fail to reject the null hypothesis.
Alternatively, find the $p$ -value using the table below: \begin{tabular}{|l|l|l|l|l|l|l|l|l|l|l|} \hline $Z$ & 0.00 & 0.01 & 0.02 & 0.03 & 0.04 & 0.05 & 0.06 & 0.07 & 0.08 & 0.09 \\ \hline-0.9 & 0.184 & 0.181 & 0.179 & 0.176 & 0.174 & 0.171 & 0.169 & 0.166 & 0.164 & 0.161 \\ \hline-0.6 & 0.274 & 0.271 & 0.268 & 0.264 & 0.261 & 0.258 & 0.255 & 0.251 & 0.248 & 0.245 \\ \hline-0.5 & 0.309 & 0.305 & 0.302 & 0.298 & 0.295 & 0.291 & 0.288 & 0.284 & 0.281 & 0.278 \\ \hline-0.4 & 0.345 & 0.341 & 0.337 & 0.334 & 0.330 & 0.326 & 0.323 & 0.319 & 0.316 & 0.312 \\ \hline-0.3 & 0.382 & 0.378 & 0.374 & 0.371 & 0.367 & 0.363 & 0.359 & 0.356 & 0.352 & 0.348 \\ \hline \end{tabular}
Select the correct answer below: Reject the null hypothesis because the value of $z$ is negative. Do not reject the null hypothesis because $|-0.52|>0.05$ . Reject the null hypothesis because the $p$ -value 0.3015 is greater than the significance level $\alpha=0.05$ . Do not reject the null hypothesis because the $p$ -value 0.3015 is greater than the significance level $\alpha=0.05$ . Reject the null hypothesis because $|-0.52|>0.05$ .

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Problem 599

The recommended daily amount of vitamin C for an adult is 80 milligrams. A pharmacist would like to test the claim that the average amount of daily vitamin C intake is different than the generally accepted amount of 80 milligrams. To test this claim, at the $1 \%$ significance level, the pharmacist collects the following data on a sample of 40 adults and records the daily intake of vitamin C. The following is the data from this study:
Sample size $=40$ adults Sample mean $=85$ milligrams From past data, it is known that the population standard deviation is 14 milligrams.
Identify the null and alternative hypothesis for this study by filling in the blanks with the correct symbol ( $=, \neq,<$ , or $>$ to represent the correct hypothesis.)
Provide your answer below: null hypothesis : $\mu \square 80$ alternative hypothesis : $\mu \square 80$

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Problem 600

Avicenna, an insurance company, offers five-year commercial property insurance policies to small businesses. If the holder of one of these policies experiences property damage in the next five years, the company must pay out $\$ 23,600$ to the policy holder. Executives at Avicenna are considering offering these policies for $\$ 791$ each. Suppose that for each holder of a policy there is a $3 \%$ chance they will experience property damage in the next five years and a $97 \%$ chance they will not.
If the executives at Avicenna know that they will sell many of these policies, should they expect to make or lose money from offering them? How much?
To answer, take into account the price of the policy and the expected value of the amount paid out to the holder. Avicenna can expect to make money from offering these policies. In the long run, they should expect to make $\square$ dollars on each policy sold. Avicenna can expect to lose money from offering these policies. In the long run, they should expect to lose $\square$ dollars on each policy sold. Avicenna should expect to neither make nor lose money from offering these policies.

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Data & Statistics

Problem 501

Dashboard14 Multiple Choice 3.5 points Courses 14/3914 / 3914/39 Calendar-11.4\%−12%-12 \%−12%12%12 \%12% 11.4%11.4 \%11.4%

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22. When the price of an inferior good rise, the substitution effect \qquad the quantity demanded and the income effect \qquad the quantity demanded. A. Decreases; decreases B. Decreases; increases C. Increases; decreases D. Increases; increases sis x2x^{2}x2 J 1 (o)Normal

Problem 521

Let xxx be a continuous random variable that follows a normal distribution with a mean of 200 and a standard deviation of 25 . Find the value of xxx so that the area under the normal curve to the right of xxx is 0.7967 .Round your answer to two decimal places. x=x=x= □\square□

Problem 522

14. If o(E′)=9:11o\left(E^{\prime}\right)=9: 11o(E′)=9:11, find p(E)p(E)p(E).15. Find the probability of choosing 7 winning spots in nine-spot keno.

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Problem 557

Find the median of the following data set. Assume the data set is a sample. 38,51,34,40,45,41,53,47,46,33,40,4238,51,34,40,45,41,53,47,46,33,40,4238,51,34,40,45,41,53,47,46,33,40,42Answer How to enter your answer (opens in new window)

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Problem 560

If XXX represents a random variable coming from a normal distribution with mean 3 and if P(X>4.1)=0.23P(X>4.1)=0.23P(X>4.1)=0.23, then P(3<X<4.1)=0.27P(3<X<4.1)=0.27P(3<X<4.1)=0.27. True False

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Problem 562

20. (C) MP. 3 Critique Reasoning There are 50 communities in Kalb County. Each community has about the same number of people. Marty estimates there are about 300 people living in each community. Is his estimate reasonable? Justify your answer.Population of Counties

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Match basketball players with respect to general athletic ability in order to test different kinds of athletic shoes. Independent Samples t-Test Related Samples t-Test

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Dashboard
14 Multiple Choice 3.5 points Courses
$14 / 39$ Calendar
-11.4\%
$-12 \%$
$12 \%$ $11.4 \%$

22. When the price of an inferior good rise, the substitution effect $\qquad$ the quantity demanded and the income effect $\qquad$ the quantity demanded. A. Decreases; decreases B. Decreases; increases C. Increases; decreases D. Increases; increases sis $x^{2}$ J 1 (o)
Normal

Let $x$ be a continuous random variable that follows a normal distribution with a mean of 200 and a standard deviation of 25 . Find the value of $x$ so that the area under the normal curve to the right of $x$ is 0.7967 .
Round your answer to two decimal places. $x=$ $\square$

14. If $o\left(E^{\prime}\right)=9: 11$ , find $p(E)$ .
15. Find the probability of choosing 7 winning spots in nine-spot keno.

Find the median of the following data set. Assume the data set is a sample. $38,51,34,40,45,41,53,47,46,33,40,42$
Answer How to enter your answer (opens in new window)

If $X$ represents a random variable coming from a normal distribution with mean 3 and if $P(X>4.1)=0.23$ , then $P(3<X<4.1)=0.27$ . True False

20. (C) MP. 3 Critique Reasoning There are 50 communities in Kalb County. Each community has about the same number of people. Marty estimates there are about 300 people living in each community. Is his estimate reasonable? Justify your answer.
Population of Counties