A television show conducted an experiment to study what happens when buttered toast is dropped on the floor. When 43 buttered slices of toast were dropped, 26 of them landed with the
buttered side up and 17 landed with the buttered side down. Use a 0.05 significance level to test the claim that toast will land with the buttered side down 50% of the time. Use the P-value
method. Use the normal distribution as an approximation to the binomial distribution. After that, supposing the intent of the experiment was to assess the claim that toast will land with the
buttered side down more than 50% of the time, write a conclusion that addresses the intent of the experiment. Let p denote the population proportion of all buttered toast that will land with the buttered side down when dropped. Identify the null and alternative hypotheses to test the claim that buttered toast
will land with the buttered side down 50% of the time.
H0:pH1:p
(Type integers or decimals. Do not round.)
Identify the test statistic
z=
(Round to two decimal places as needed.)
Identify the P-value.
P-value =
(Round to three decimal places as needed.)
State the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim.
the null hypothesis. There sufficient evidence to
the claim that buttered toast will land with the buttered side down 50% of the time.
Write a conclusion that addresses the test that the toast will land with the buttered side down more than 50% of the time.
The intent of the experiment was to test H0:p
and H1:p. Based on these results, there sufficient evidence to support of the claim that buttered toast will land with the
buttered side down more than 50% of the time.
(Type integers or decimals. Do not round.)
Question 6 of 6 (1 point) I Question Attempt: 1 of Unlimited
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Español Unhealthy Days in Cities The number of unhealthy days based on the AQI (Air Quality Index) for a random sample of metropolitan areas is shown. Construct an 89% confidence interval based on the data. Assume the variable is normally distributed. Use a graphing calculator and round the answers to at least one decimal place.
39321016292401
Send data to Excel
□<μ<□
For this discussion, you will compare these two categories of statistics, and explain which you feel is the most important to the biological sciences.
Develop a main response in which you address the following:
• Briefly summarize the main functions of descriptive and inferential statistics.
• Identify which you feel is the most useful in the biological sciences.
• Explain your position, providing supporting evidence from the textbook, other scholarly sources, and/or examples where possible.
Pew Research Center recently conducted a survey on the practice of tipping at restaurants.
Researchers determined that 81% of all adults in the United States always leave a tip when
eating at a restaurant with an average tip amount of $7.49. A restaurant manager wonders if
this is true for his restaurant, so he analyzes a random sample of 100 recent bills. He finds that
90% of bills included a tip for an average tip amount of $10.25.
a. Which values are statistics? Use appropriate notation.
b. Which values are parameters? Use appropriate notation.
Use the sample data and confidence level given below to complete parts (a) through (d).
A research institute poll asked respondents if they felt vulnerable to identity theft. In the poll, n=912 and x=596 who said "yes." Use a 99% confidence level.
Click the icon to view a table of z scores.
a) Find the best point estimate of the population proportion p.
0.654
(Round to three decimal places as needed.)
b) Identify the value of the margin of error E.
E=0.041
(Round to three decimal places as needed.)
c) Construct the confidence interval.
0.614<p<0.694
(Round to three decimal places as needed.)
d) Write a statement that correctly interprets the confidence interval. Choose the correct answer below.
A. 99% of sample proportions will fall between the lower bound and the upper bound.
B. One has 99% confidence that the sample proportion is equal to the population proportion.
C. One has 99% confidence that the interval from the lower bound to the upper bound actually does contain the true value of the population proportion.
D. There is a 99% chance that the true value of the population proportion will fall between the lower bound and the upper bound.
At a certain college, it is estimated that at most 32% of the students ride bicycles to class. Does this seem to be a valid estimate if, in a random sample of 98 college students, 39 are found to ride bicycles to class? Use a 0.01 level of significance.
Click here to view page 1 of the standard normal distribution table.
Click here to view page 2 of the standard normal distribution table. Let a success be a student that rides a bicycle to class. Identify the null and alternative hypotheses.
A. H0: p=0.32H1: p<0.32 B. H0: p=0.32H1: p=0.32 C. H0: p>0.32H1: p=0.32 D. H0: p<0.32H1: p=0.32 E. H0: p=0.32H1: p=0.32 F. H0: p=0.32H1: p>0.32 Identify the critical region. Select the correct choice below and fill in the answer box(es) to complete your choice.
(Round to two decimal places as needed.)
A. z<
B. z< or z>
C. z>2.33 Find the test statistic.
z= (Round to two decimal places as needed.)
Question 17
2 pts The success/failure condition for a confidence interval for proportions requires there to be:
at most 10 success and at most 10 failures
at least 10 success and at least 10 failures
Find the cross-price elasticity of demand for strawberries when quantity drops from 1,800 to 1,550 as price falls from \$2.35 to \$2.15. Round to the nearest hundredth.
In a survey of 2379 adults in a recent year, 1314 say they have made a New Year's resolution.
Construct 90% and 95% confidence intervals for the population proportion. Interpret the results and compare the widths of the confidence intervals. The 90% confidence interval for the population proportion p is (□,□).
(Round to three decimal places as needed.) The 95% confidence interval for the population proportion p is (□,□).
(Round to three decimal places as needed.) With the given confidence, it can be said that the ______ of adults who say they have made a New Year's resolution is ______ of the given confidence interval. Compare the widths of the confidence intervals. Choose the correct answer below. A. The 90% confidence interval is wider.
B. The 95% confidence interval is wider.
C. The confidence intervals cannot be compared.
D. The confidence intervals are the same width.
You are given the sample mean and the population standard deviation. Use this information to construct the 90% and 95% confidence intervals for the population mean. Interpret the results and compare the widths of the confidence intervals. If convenient, use technology to construct the confidence intervals.
A random sample of 45 home theater systems has a mean price of $146.00. Assume the population standard deviation is $15.40. Construct a 90% confidence interval for the population mean.
The 90% confidence interval is ().
(Round to two decimal places as needed.) Construct a 95% confidence interval for the population mean.
The 95% confidence interval is ().
(Round to two decimal places as needed.) Interpret the results. Choose the correct answer below.
A. With 90% confidence, it can be said that the sample mean price lies in the first interval. With 95% confidence, it can be said that the sample mean price lies in the second interval. The 95% confidence interval is wider than the 90%.
B. With 90% confidence, it can be said that the population mean price lies in the first interval. With 95% confidence, it can be said that the population mean price lies in the second interval. The 95% confidence interval is narrower than the 90%.
C. With 90% confidence, it can be said that the population mean price lies in the first interval. With 95% confidence, it can be said that the population mean price lies in the second interval. The 95% confidence interval is wider than the 90%.
Fall ' 24
(Ch 8-9) Earn 5 E.C if
Question 18, 9.2.14-T
HW Score: 74.06%,17.03 of 23 points
Part 4 of 6
Points: 0 of 1
Sav The IQ scores for a random sample of subjects with low lead levels in their blood and another random sample of subjects' with high lead levels in their blood were collected. The statistics are summarized in the accompanying table. Assume that the two samples are independent simple random samples selected from normally distributed populations. Do not assume that the population standard deviations are equal. Complete parts (a) to (c).
\begin{tabular}{|c|c|c|c|c|}
\hline & μ & n & x & s \\
\hline Low Lead Level & μ1 & 89 & 92.61392 & 15.97262 \\
\hline High Lead Level & μ2 & 26 & 87.47604 & 9.56479 \\
\hline
\end{tabular}
a. Use a 0.01 significance level to test the claim that the mean IQ score, of people with low blood lead levels is higher than the mean IQ score of people with high blood lead levels. What are the null and altemative hypotheses? Assume that population 1 consists of subjects with low lead levels and population 2 consists of subjects with high lead levels.
A. H0:μ1=μ2
B. H0:μ1=μ2H1:μ1=μ2H1:μ1>μ2 C. H0:μ1≤μ2
D.
H0:μ1=μ2H1:μ1>μ2H1:μ1>μ2 The test statistic is 2.03 . (Round to two decimal places as needed.)
The P-value is 0.023 . (Round to three decimal places as needed.)
State the conclusion for the test.
A. Reject the null hypothesis. There is sufficient evidence to support the claim that subjects with low lead levels have higher IQ scores.
B. Fail to reject the null hypothesis. There is not sufficient evidence to support the claim that subjects with low lead levels have higher IQ scores.
C. Reject the null hypothesis. There is not sufficient evidence to support the claim that subjects with low lead levels have higher IQ scores.
D. Fail to reject the null hypothesis. There is sufficient evidence to support the claim that subjects with low lead levels have higher IQ scores.
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Compute the standard error and the bound on the error of estimation associated with p^ using the finite population correction factor when:
- N=1000,n=100p=0.35
- N=2000,n=100p=0.45
- N=5000,n=200p=0.25
- N=10000,n=500p=0.60
- N=50000,n=1000p=0.55
Assuming that the Central Limit Theorem applies to the sampling distribution of p∧, approximate the probability that p∧ is within:
1.5 standard errors of p
2.5 standard errors of p
Question 36
0/1 pt
3
99
Details You are performing a left-tailed test with test statistic z=−1.06, find the p -value to 4 decimal places
□
Question Help:
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Unhealthy Days in Cities The number of unhealthy days based on the AQI (Air Quality Index) for a random sample of metropolitan areas is shown. Round the sample statistics and final answers to at least one decimal place.
29231032240527
Send data to Excel Construct a 98% confidence interval based on the data. Assume the variable is normally distributed.
8.498<μ<35.018
4. Use the large sample confidence interval formula to compute a :
- 95% lower bound confidence interval for p when n=350 and p^=0.46
- 99% lower bound confidence interval for p when n=250 and p^=0.82
- 95% lower bound confidence interval for p when n=198 and p^=0.56
- 99% lower bound confidence interval for p when n=955 and p^=0.71
5) A group of students measured the lengths of all the carrots in a five-pound bag of baby carrots. They calculated the average length of baby carrots to be 2.0 inches with a standard deviation of 0.25 inches. Suppose we randomly survey 16 fivepound bags of baby carrots. Find the probability that xˉ is between two and 2.25 inches.
a. 0.5000
C. 0.3413
b. 0.2500
d. 0.8413
8. What can be said about the validity of the p-value computed in a t-test when the normal probability plot clearly does not support the assumption of normality? If the normal probability plot shows that the normality assumptions isn't met, the p-value from t-test is invalid, we can not trust it to accurately reflect the probability of observing our results if there's no real difference between the groups.
The Harris poll conducted a survey in which they asked, "How many tattoos do you currently have on your body?"Of the 1100 males surveyed, 183 responded that they had at least 1 tattoo. Conduct a hypothesis test, using the α=0.05 level of significance, to determine whether the proportion of males that have at least one tattoo differs from the proportion of females that have at least one tattoo. State the null and alternative hypotheses; then state the conclusion of the test in the context of the problem.Of the 1000 females surveyed, 133 responded that they have at least one tattoo.
Question 8
0/3 pts
Details Out of 100 people sampled, 31 had kids. Based on this, construct a 95% confidence interval for the true population proportion of people with kids. Give your answers as decimals, to three places.
□<p<□
You are conducting a two-tailed test of a claim about a population mean when sigma is known. You also have statistics from a sample of 7. If α=0.1, find the positive critical value, to two decimal places.
Assume that hybridization experiments are conducted with peas having the property that for offspring, there is a 0.75 probability that a pea has green pods. Assume that the offspring peas are randomly selected in groups of 20. Complete parts (a) through (c) below.
c. Is a result of 18 peas with green pods a result that is significantly high? Why or why not? The result □ significantly high because 18 peas with green pods is □□ peas.
4. An appropriate fiscal policy (سياسة حكومية مناسبة) for severe demand-pull inflation is:
A. An increase in government spending.
B. Depreciation of the dollar.
C. A reduction in interest rates.
D. A tax rate increase.
(5) 2. A group of 894 women aged 70−79 had their height and weight measured. The mean height
d. What percentage of the population is expected of weigh between 55 and 75 kg ? deviation of 12.7 kstandard deviation of 5 cm and the mean weight was 65.9 kg with a standard
a. Suppose you were asked for a range of typical heights and weights for this population of 9round terwewes would you give? Explain.
9
=25.4 around bewremn 40 sig and 91.31 gg
+75.491.325.4405
b. Which of the two measurements appears more variable? Explain. The weight measurnents are more vorate
because 12.7>5
A normally distributed set of data has been generated where 50% of the data lies below 97 and 70% lies below 104. Determine the mean and standard deviation of this data.
If the correlation r=0, what does this indicate about the relationship between two quantitative variables? A. Strong linear B. No linear C. Strong relationship D. No relationship
Given the weight prediction formula Weight=−115+3.6(Height), which statements are true? A. I only B. II and III only C. I and II only D. III only E. II only. Select one.
Determine whether the given correlation coefficient is statistically significant at the specified level of significance and sample size.
r=0.183,α=0.01,n=30 Answer
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Yes, the correlation coefficient is statistically significant
No, the correlation coefficient is not statistically significant
The following data gives the number of hours 7 students spent studying and their corresponding grades on their midterm exams.
\begin{tabular}{|c|c|c|c|c|c|c|c|}
\hline Hours Spent Studying & 0 & 0.5 & 1 & 3.5 & 4 & 5 & 5.5 \\
\hline Midterm Grades & 63 & 72 & 75 & 81 & 84 & 90 & 93 \\
\hline
\end{tabular}
Copy Data Step 1 of 3 : Calculate the correlation coefficient, r. Round your answer to six decimal places. Answer
Tables
Keypad How to enter your answer (opens in new window)
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A manufacturer of colored candies states that 13% of the candies in a bag should be brown, 14% yellow, 13% red, 24% blue, 20% orange, and 16% green. A student randomly selected a bag of colored candies. He counted the number of candies of each color and obtained the results shown in the table. Test whether the bag of colored candies follows the distribution stated above at α=0.05 level of significance. Using the level of significance α=0.05, test whether the color distribution is the same. Click here to view the table. Click here to view the table of critical values of the chi-square distribution. C. H0: The distribution of colors is at least as uniform as stated by the manufacturer.
H1: The distribution of colors is less uniform than stated by the manufacturer. D. H0: The distribution of colors is the same as stated by the manufacturer.
H1: The distribution of colors is not the same as stated by the manufacturer. Compute the expected counts for each color. (Round to two decimal places as needed.)
A random sample of 1024 adults in a certain large country was asked "Do you pretty much think televisions are a necessity or a luxury you could do without?" Of the 1024 adults surveyed, 522 indicated that televisions are a luxury they could do without. Complete parts (a) through (e) below.
Click here to view the standard normal distribution table (page 1).
Click here to view the standard normal distribution table (page 2). (a) Obtain a point estimate for the population proportion of adults in the country who believe that televisions are a luxury they could do without.
p=
(Round to three decimal places as needed.) (b) Verify that the requirements for constructing a confidence interval about p are satisfied.
The sample a simple random sample, the value of is , which is less than or equal to 5% of the .
⋅10, and the
(Round to three decimal places as needed.) (c) Construct and interpret a 95% confidence interval for the population proportion of adults in the country who believe that televisions are a luxury they could do without. Select the correct choice below and fill in any answer boxes within your choice.
(Type integers or decimals rounded to three decimal places as needed. Use ascending order.)
A. We are % confident the proportion of adults in the country who believe that televisions are a luxury they could do without is between and .
B. There is a % probability the proportion of adults in the country who believe that televisions are a luxury they could do without is between and . (d) Is it possible that a supermajority (more than 60%) of adults in the country believe that television is a luxury they could do without? Is it likely?
It is that a supermajority of adults in the country believe that television is a luxury they could do without because the 95% confidence interval .
(Type an integer or a decimal. Do not round.) (e) Use the results of part (c) to construct a 95% confidence interval for the population proportion of adults in the country who believe that televisions are a necessity.
Lower bound: Upper bound:
(Round to three decimal places as needed.)
The operations manager of a company that manufactures tires wants to determine whether there are any differences in the quality of work among the three daily shifts. She randomly selects 300 tires and carefully inspects them. Each tire is either classified as perfect, satisfactory, or defective, and the shift that produced it is also recorded. The two categorical variables of interest are "shift" and "condition of the tire produced". The p-value of the Chi-Squared test of independence is 0.073. Does the data provide sufficient evidence at the 5% significance level to infer that there are differences in quality among the three shifts? No, the manager cannot conclude that there are differences in quality among the three shifts. Yes, the manager can conclude that there are differences in quality among the three shifts. The p-value is too close to 5%, so this is a borderline case. The manager needs to inspect more tires to be able to make a conclusion.
Q#1) A. A random sample of 25 items is taken from normal
population, producing a sample mean of 65 with standard
deviation 3. determine the sample error, standard error, and
construct a 90% confidence interval for the population mean.
interpret your answer
B. Determine the sample size necessary to estimate the
population mean with standard deviation 36 to ensure a 95%
confidence in the result and to be within 5 of the true population
mean. How can reduce the sample error
Q#2) Suppose you are working with a data set that is normally
distributed, with a mean of 100 and a standard deviation of 24. If
a random sample of 64 is taken, a. probability of x Greater than 65
b. probability of X Less than 130
c. probability of X Between 80 and 140
d. what is the probability that the sample mean is Greater than 110
e. what is the probability that the sample mean is less than 85
The average level of dissolved oxygen in a stream or river is an important indicator of the water's ability to
support aquatic life. A researcher measures the DO level at 27 randomly chosen locations along a stream.
Below are the results in mg/l:
5.26 5.13 4.7 2.91 4.9
4.8 3.86 5.72 5.2 4.46
5.01 5.67 4 3.87 4.47
2.96 3.92 4.25 3.64 4.73
4.4 5.61 5.21 5.32 4.45
4.96 4.57
The average level of dissolved oxygen less than 5 mg/l puts aquatic life at risk. At 1% significance level can
we conclude that an average level of dissolved oxygen less than 5 mg/l? We may also assume that the
sample is from a normal population. (Note: The average and the standard deviation of the data are
respectively 4.59 mg/l and 0.75 mg/l.) Procedure: One variance χ2 Hypothesis Test Hint: In the question, look for the keywords such as mean/average, proportion/percentage,
variance/standard deviation! Assumptions: (select everything that applies)
Simple random sample
Population standard deviation is unknown
Normal population
The number of positive and negative responses are both greater than 10
Population standard deviation is known
Sample size is greater than 30 Step 1. Hypotheses Set-Up:
H0: Select an answer = ____ , where Select an answer is the Select an answer and the units are Select an answer
Ha: Select an answer ? ____ , and the test is Select an answer Step 2. The significance level α = ____ %
A research firm conducted a poll in March 2020 among a random national sample of 480 adults. In the poll,
134 Americans approve of the president's management of the crisis. At 10% significance level, test the claim
that the percentage of the Americans that approve the president's management of the crisis is less than
30%. Procedure: Select an answer Assumptions: (select everything that applies)
☐ The number of positive and negative responses are both greater than 10
☐ Normal population
☐ Population standard deviation is unknown
☐ Sample size is greater than 30
☐ Simple random sample
☐ Population standard deviation is known
A sample of birth weights of 12 girls was taken. Below are the results (in g): 3659.6 3408 2527.8 4064.9 3585.1
2947.1 3441.8 4250.2 2872 2759.8
3648.5 3788.5 (Note: The average and the standard deviation of the data are respectively 3412.8 g and 533.7 g.) Use a 10% significance level to test the claim that the standard deviation of birthweights of girls is greater than the standard deviation of birthweights of boys, which is 510 g. Procedure: One variance χ2 Hypothesis Test Assumptions: (select everything that applies)
* Simple random sample
* Normal population Step 1. Hypotheses Set-Up:
H0: σ2=260100 , where σ is the population standard deviation and the units are g.
Ha: σ2>260100 , and the test is Right-Tailed Step 2. The significance level α=10% Step 3. Compute the value of the test statistic: Step 4. Testing Procedure: (Round the answers to 3 decimal places)
CVA
Provide the critical value(s) for the Rejection Region:
left CV is and right CV is
PVA
Compute the P-value of the test statistic:
P-value is
Multiple Choice 10 points
A test of significance produces a p-value of .03. Which of the following conclusions is appropriate?
Accept Ha at a significance level of 5%
Accept H0 at a significance level of 5%
Reject Ha at a significance level of 5%
Reject H0 at a significance level of 5%
21. (8 points) Prior research suggests that youth mentoring reduces children's behavior problems. interested in testing this hypothesis. He assessed a few at-risk children's aggressive problems using a standardized scale called Child Behavior Checklist before they ent mentoring program and one year after they entered the program. Below is the data he
\begin{tabular}{|c|c|c|}
\hline Child ID & \begin{tabular}{l}
Aggressive behavior \\
problems before the \\
mentoring program
\end{tabular} & \begin{tabular}{l}
Aggressive behavior problems \\
one year after the mentoring \\
program
\end{tabular} \\
\hline 1101 & 63 & 59 \\
\hline 1102 & 64 & 67 \\
\hline 1103 & 60 & 56 \\
\hline 1104 & 58 & 52 \\
\hline 1105 & 59 & 60 \\
\hline 1106 & 60 & 58 \\
\hline
\end{tabular}
a. What test statistics would you calculate if you are to conduct a 5-step hypothes why do you choose this test?
Listed below are the numbers of words spoken in a day by each member of eight different randomly selected couples. Complete parts (a) and (b) below.
\begin{tabular}{lcccccccc}
\hline Male & 15,554 & 27,435 & 1428 & 7938 & 19,085 & 14,960 & 13,905 & 26,089 \\
\hline Female & 24,092 & 13,465 & 17,815 & 17,337 & 13,237 & 17,233 & 16,889 & 17,968 \\
\hline
\end{tabular}
sufficient evidence to support the claim that males speak fewer words in a day than females.
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 □ word(s) <μd<□ word(s).
(Round to the nearest integer as needed.)
What feature of the confidence interval leads to the same conclusion reached in part (a)?
Since the confidence interval contains □□ the null hypothesis.
Arroyo Seco and Stone Mountain are schools in different states. The heights of students at Arroyo Seco have a population mean of 65.5 inches and a standard deviation of 4.7 inches. The heights of students at Stone Mountain have a population mean of 53.5 inches with a standard deviation of 1.3 inches. For each school, the distribution of the heights of students is clearly skewed (not approximately symmetric). Manuel is a student at Arroyo Seco and is 60 inches tall. Frank is a student at Stone Mountain and is 51 inches tall.
(a) Find the z-scores of Manuel's height as a student at Arroyo Seco and Frank's height as a student at Stone Mountain. Round your answers to two decimal places.
z-score of Manuel's height: □
z-score of Frank's height: □
(b) Relative to his population, which student is taller? Choose the best answer based on the z-scores of the two heights.
Manuel
Frank
It is unclear which student is taller relative to his population
Lejuan fit a linear function to some data. He then plotted the residuals in the graph on the right. Is the linear function a good fit for this data? Explain your answer using what you've learned about residuals.
The linear function is a good fit for the data.
The linear function is not a good fit for the data.
H07928206
This test: 26 point(s) possible
This question: 2 point(s) possible
Submit test
Question 8 of 12 Use the range rule of thumb to identity the values that are significantly low, the values that are signficantly high, and the values that are neither significantly low nor significantly high. significantly high. What test scores are significantly low? Select the correct answer below and fill in the answer box(es) to complete your choice.
A. Test scores that are greater than □ (Round to one decimal place as needed)
B. Test scores that are between □ and □ (Round to one decimal place as needed. Use ascending order.)
C. Test scores that are less than □ (Round to one decimal place as needed.) What test scores are significantly high? Select the correct answer below and fill in the answer box(es) to complete your choice.
A. Test scores that are greater than □□ . (Round to one decimal place as needed.)
B. Test scores that are less than □ . (Round to one decimal place as needed.)
(1) Time Limit: 05:00:00
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The accompanying table shows the technology output for a test using data on the pulse rates of several hundred people to see whether men or women tended to have higher pulse rates. The data are random and independent. Complete parts (a) and (b) below. Click the icon to view the technology output.
b. Use the technology output to test the hypothesis that the pulse rates for men and women are not equal, using a significance level of 0.05 . The samples are large enough so that Normality is not an issue. Determine the hypotheses for this test. Let μ be the population mean pulse rate. Choose the correct answer below.
A. H0:μwomen =μmen B. H0:μwomen >μmen C. H0:μwomen <μmen Ha:μwomen >μmen Ha:μwomen =μmen
D.
H0:μwomen =μmen Ha:μwomen =μmen
E. H0:μwomen =μmen F. H0:μwomen =μmen Ha:μwomen <μmen Ha:μwomen =μmen Find the test statistic for this test.
t=3.39 (Type an integer or a decimal. Do not round.)
Find the p-value for this test.
p-value =0.001 (Type an integer or a decimal. Do not round.)
What is the conclusion for this test?
A. Do not reject H0. At the 5% significance level, there is insufficient evidence to conclude that the mean pulse rate of men is different from the mean pulse rate of women.
B. Do not reject H0. At the 5% significance level, there is sufficient evidence to conclude that the mean pulse rate of men is different from the mean pulse rate of women.
C. Reject H0. At the 5% significance level, there is insufficient evidence to conclude that the mean pulse rate of men is different from the mean pulse rate of women.
D. Reject H0. At the 5% significance level, there is sufficient evidence to conclude that the mean pulse rate of men is different from the mean pulse rate of women.
4. DETAILS
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PECKSTAT2ACC 3.5.050.MI.
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test and 70 on the second test. Use z-scoresto determine on which exam the student performed better relative to the other test takers.
first exam
second exam
Submit Answer
1a. Are egg consumption and population size proportional in Republica and the U.S.? Show calculations and state your conclusion.
1b. If proportional, how many eggs would 86 million people consume? If not, explain which country prefers eggs more.
Fit a regression line to the data and find the correlation coefficient. Predict life expectancy in 2020 using x as decades after 1900. Choose the correct line: A. y=48.08x+0.750, B. y=0.750x−48.08, C. y=0.750x+48.08, D. y=48.08.
Fit a regression line to the data, find the correlation coefficient, and predict life expectancy in 2020 using x as decades after 1900. Choose the correct regression line: A. y=48.08x+0.750 B. y=0.750x−48.08 C. y=0.750x+48.08 D. y=48.08. Round the correlation coefficient to three decimal places.
```latex
\textbf{EXPERIENCE COLLEGE BEFORE COLLEGE} \textbf{7. Circle the correct options below to complete the conclusion.} After conducting a one / two -tailed paired t-test, we can conclude that we should fail to reject / reject our null hypothesis. There is / There is not a difference in the creatine phosphate generated by nerve cells when damaged. (Our p-value is greater than / less than 0.05). \textbf{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.} \textbf{Dialogue Transcript:} \textbf{assistant:} Hello! It looks like you need help with a conclusion for a statistical test problem. To provide the correct completion for the conclusion, I'll need to know: 1. Was a one-tailed or two-tailed paired t-test conducted? 2. What is the p-value obtained from the test? 3. What is the null hypothesis you're testing? With this information, I can guide you on how to fill in the blanks correctly. Looking forward to your response! \textbf{user:} I uploaded an image and extracted the following:
* Text: Regeneration Data: Here are the data for the 10 monkeys. Conduct a paired t-test to answer the following questions.
\begin{tabular}{|l|l|l|}
\hline
Monkey ID & CP on Left & CP on Right \\
\hline
1 & 15.6 & 12.5 \\
\hline
2 & 8.6 & 9.4 \\
\hline
3 & 24.1 & 18.2 \\
\hline
4 & 15.7 & 9.8 \\
\hline
5 & 5.3 & 3.6 \\
\hline
6 & 11.1 & 12.9 \\
\hline
7 & 13.8 & 7.3 \\
\hline
8 & 15.5 & 14.9 \\
\hline
9 & 8.7 & 8.5 \\
\hline
10 & 28.4 & 23.9 \\
\hline
\end{tabular} 4. On average, how much difference in CP production was observed between the damaged and undamaged nerves? (Round to 2 decimal places and report the absolute value. Use this rounded value for all subsequent calculations.)
1025.4=2.54 5. What is the standard error for the test? You are given Sdiff =3.02. (Round to 3 decimal places. Use this rounded value for all subsequent calculations.)
103.02≈3.1623.02=0.955 6. What is the test statistic? (Round to 2 decimal places and report the absolute value.)
0.9552.54=2.66 \textbf{assistant:} Great! You have already calculated several components needed for the paired t-test. Now, we just need to finalize the steps by determining if you should reject or fail to reject the null hypothesis. For that, we need to know the p-value and whether you're using a one-tailed or two-tailed test. Let's proceed with the steps: 1. \textbf{Determine the critical value and p-value}: You need to compare your test statistic to a critical value from a t-distribution or use the test statistic to find a p-value. This will typically depend on your degree of freedom (here, n−1=10−1=9) and the significance level, often 0.05. 2. \textbf{Establish the null hypothesis}: The null hypothesis usually states that there is no difference in CP production between the damaged and undamaged nerves. Could you specify if you have a one-tailed or two-tailed test and provide the p-value or significance level? This will enable us to make the concluding decision for you. Once you provide that, we can complete the conclusion statement! \textbf{user:} One
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For the following claim, state the null and alternative hypothesis.
A research study concludes that the high school graduation rate in the United States is higher than the high school graduation rate in Europe, Let p1 represent the high school graduation rate in the United States. The null hypothesis is H0 : □ . The alternative hypothesis is H1 : □ . p1p2
Children were randomly assigned to one of two groups: One group enrolled in a certain preschool, and one did not enroll. Follow-up studies were d decades to answer the research question of whether attendance at preschool had an effect on high school graduation. The data can be divided to whether the preschool attendance effect is different for males and females. The table shows a summary of the data for females,
□ Click the icon to view the technology output.
\begin{tabular}{ccc}
& Preschool & No Preschool \\
HS Grad & 26 & 7 \\
HS Grad No & 3 & 17
\end{tabular} Compare the graduation rate for those females who went to preschool with the graduation rate for females who did not go to preschool.
A. The graduation rate is higher for those females who did not go to preschool.
B. The graduation rates are the same.
C. The graduation rate is higher for those females who went to preschool.
(b) Test the hypothesis that preschool and graduation rate are associated, using a significance level of 0.05. Choose the correct null hypothesis (H0) and alternative hypothesis (Ha).
The following three independent random samples are obtained from three normally distributed populations with equal variances. The dependent variable is starting hourly wage, and the groups are the types of position (internship, co-op, work study). We are testing the claim that position is a factor in starting salaries for new college graduates. at α=0.1 given the following data
\begin{tabular}{|c|c|c|}
\hline Group 1: Internship & Group 2: Co-op & Group 3: Work Study \\
\hline 13 & 9.5 & 17.75 \\
\hline 11.5 & 11.5 & 13.75 \\
\hline 10 & 9 & 12.75 \\
\hline 13.75 & 13 & 13.5 \\
\hline 14 & 12.75 & 12.75 \\
\hline 14.25 & 9.5 & 14.75 \\
\hline 11 & 15.75 & 12.25 \\
\hline 11 & 12.5 & 14.5 \\
\hline
\end{tabular} 1. Your friend Maia helped you with the null and alternative hypotheses...
H0:μ1=μ2=μ3H1 : At least two of the means differ from each other. 2. For this study, we should use
Select an answer 3. The test-statistic for this data =□ (Please show your answer to 3 decimal places.) 4. The p-value for this sample =□ (Please show your answer to 4 decimal places.) 5. The p-value is Select an answer
□α 6. Base on this, we should Select an answer 7. As such, the final conclusion is that...
There is insufficient evidence to support the claim that position is a factor in starting salaries for new college graduates.
There is sufficient evidence to support the claim that position is a factor in starting salicries for new college graduates.
2uestion 17 Analysts expect a dividend per share equal to £0.5 for Company X. However, the actual dividend was £0.2.
Which of the following is true according to the dividend signalling theory?
A. Stock price will not change
B. The company is committed to pay the remaining £0.1 as additional dividend in the future
C. The stock has a negative beta ( β )
D. Stock price will decrease
Time left 0:13:13 Please answer Questions 1-5 based on the following.
An online retailer has decided to develop a simple linear regression model to predict the weekly demand for a product based on its price (£). A sample of 36 consecutive weeks is selected. The results of the regression analysis performed by Excel are provided below: SUMMARY OUTPUT
\begin{tabular}{lr}
\hline \multicolumn{2}{c}{ Regression Statistics } \\
\hline Multiple R & 0.8134 \\
R Square & 0.6615 \\
Adjusted R Square & 0.6516 \\
Standard Error & 23.981 \\
Observations & 36 \\
\hline
\end{tabular} ANOVA
\begin{tabular}{lrrrrr}
\hline & df & \multicolumn{1}{l}{ SS } & \multicolumn{1}{l}{ MS } & F & Significance F \\
\hline Regression & 1 & 38,219 & 38,219 & 66.46 & 0.0000 \\
Residual & 34 & 19,554 & 575 & & \\
Total & 35 & 57,773 & & & \\
\hline
\end{tabular}
\begin{tabular}{lrrrrrr}
\hline & Coefficients & Standard Error & t Stat & P-value & Lower 95\% & Upper 95\% \\
\hline Intercept & 257.65 & 20.95 & 12.30 & 0.0000 & 215.08 & 300.21 \\
Price & -11.26 & 1.38 & -8.15 & 0.0000 & -14.06 & -8.45 \\
\hline
\end{tabular} Internret the meaning of the confficient for Price?
1. SAT scores for High School A are approximately normally distrio deviation 105. SAT scores for High School B are approximately normally distributed with mean 1200 and standard deviation 125. A random sample of 15 SAT scores from High School A is selected and the sample mean xˉA is calculated. A separate random sample of 12 SAT scores from High School B is selected and the sample mean xˉB is calculated.
a. Describe the shape of the sampling distribution of xˉA−xˉB. Justify.
b. What is the mean of the sampling distribution of xˉA−xˉB ? Interpret
c. What is the standard deviation of the sampling distribution of xˉA−xˉB ? Be sure to check the 10% condition.
d. What is the probability that the sample mean of High School A is greater than the sample mean from High School B?
Wordle is a popular online game in the New York Times. To win, you must correctly guess a 5-letter word in 6 attempts or less. The hardest word to date was JAZZY. For all people that correctly solved JAZZY, the mean was 5.82 attempts with a standard deviation of 0.56 attempts.
a. Can we assume the population shape for number of attempts to correctly solve JAZZY is approximately normal? Why or why not?
b. Separate random samples of 32 AP Statistics students and 45 AP Calculus students who correctly solved JAZZY will be selected, and the average number of attempts to solve will be calculated for each sample ( xˉS and xˉC ). Assuming both groups have a mean of 5.82 attempts and a standard deviation of 0.56 attempts, describe the sampling distribution of xˉS−xˉC.
c. Find P(xˉS−xˉC≤−0.3).
d. Suppose the sample mean for the AP Statistics students is 5.1 attempts and the sample mean for the AP Calculus students is 5.4 attempts. Does this result provide convincing evidence that AP Statistics students can correctly guess the word JAZZY in fewer attempts than AP Calculus students, on average?
\begin{tabular}{cc}
Dozen Eggs & Gallon of Milk \\
\hline 1.28 & 3.18 \\
1.13 & 3.23 \\
1.16 & 3.23 \\
1.19 & 3.21 \\
1.14 & 3.12 \\
1.17 & 3.09 \\
1.17 & 3.14 \\
1.28 & 3.13 \\
1.26 & 3.17 \\
1.28 & 3.21
\end{tabular}
Send data to Excel Part: 0/3 Part 1 of 3 Compute the least-squares regression line for predicting the price of milk from the price of eggs. Round the slope and y-intercept to at least four decimal places.
Which of the following is a true statement?
(1 point)
The slope of the line of best fit indicates that movie ticket prices tend to increase by about \$1.52 per year since 1974.
The slope of the line of best fit indicates that movie ticket prices tend to increase by about \$0.25 per year since 1974. The slope of the line of best fit indicates that movie ticket prices tend to decrease by about \$0.25 per year since 1974. There is a positive association between the number of years that have passed between 1974 and the price of a movie ticket.
The population mean and standard devia are given below. Find the required probab and determine whether the given sample would be considered unusual. For a sample of n=65, find the probability of a sample mean being greater than 212 if μ=211 and σ=5.7.
Decide whether you can use the normal distribution to approximate the binomial distribution. If you can, use the normal distribution to approximate the indicated probabilities and sketch their graphs. If you cannot, explain why and use the binomial distribution to find the indicated probabilities.
A survey of adults found that 6\% say their favorite sport is auto racing. You randomly select 300 adults and ask them to name their favorite sport. Complete parts (a) through (d).
OINTS)
THE GLEASON SUPERMARKET'S MANAGER MUST DECIDE HOW MUCH OF EACH ICE CREAM FLAVOR HE SHOULD STOCK SO THAT CUSTOMER DEMANDS ARE SATISFIED BUT UNWANTED FLAVORS DON'T RESULTIN WASTE. THE ICE CREAM SUPPLIER CLAIMS THAT AMONG THE FOUR MOST POPULAR FLAVORS, CUSTOMERS HAVE THESE PREFERENCE RATES: 62% PREFER VANILLA, 18\% PREFER CHOCOLATE, 12% PREFER NEAPOLITAN, AND 8\% PREFER VANILLA FUDGE. A RANDOM SAMPLE OF 200 CUSTOMERS PRODUCES THE RESULTS BELOW. AT THE α=0.05 SIGNIFICANCE LEVEL, TEST THE CLAIM THAT THE SUPPLIER HAS CORRECTLY IDENTIFIED CUSTOMER PREFERENCES.
\begin{tabular}{|l|c|c|c|c|}
\hline FLAVOR & VANILLA & CHOCOLATE & NEAPOLITAN & VANILLA FUDGE \\
\hline CUSTOMERS & 120 & 40 & 18 & 22 \\
\hline
\end{tabular}
What is the main purpose of ANOVA?
To identify relationships between categorical variables.
To compare only two means, and no more.
To use the z-distribution table to calculate percentiles.
To simultaneously compare more than two means.
View Policies Current Attempt in Progress
Assume the sample is a random sample from a distribution that is reasonably normally distributed and we are doing inference for a sample mean. Find endpoints of a t-distribution with 1% beyond them in each tail if the sample has size n=18. Round your answer to three decimal places.
endpoints =±□
A hypothesis test is to be performed. Determine the null and alternate hypotheses.
In 1990, the average duration of long-distance telephone calls originating in one town was 6.5 minutes. A long-distance telephone company wants to perform a hypothesis test to determine whether the average duration of long-distance phone calls has changed from the 1990 mean of 6.5 minutes.
H0:μ=6.5 minutes H1:μ<6.5 minutes H0:μ=6.5 minutes H1:μ>6.5 minutes H0:μ=6.5 minutes H1:μ=6.5 minutes H0:μ=6.5 minutes H1:μ=6.5 minutes
Correlation and Simple Linear Regression
Performing a simple linear regression
0/5
Ghadeer You are the owner of Fast Break, a popular local place that sells drinks, snacks, and sandwiches. For inventory management purposes, you are examining how the weather affects the amount of hot chocolate sold in a day. You are going to gather a random sample of 7 days showing that day's high temperature (denoted by X, in ∘C ) and the amount of hot chocolate sold that day (denoted by Y, in liters). You will also note the product X⋅Y of the temperature and amount of hot chocolate sold for each day. (These products are written in the row labeled " XY ").
(a) Click on "Take Sample" to see the results for your random sample.
Take Sample
\begin{tabular}{|c|c|c|c|c|c|c|c|}
\hline \begin{tabular}{c}
High temperature, X \\
(in ∘C )
\end{tabular} & 25 & 3 & 19 & 29 & 8 & 14 & 34 \\
\hline \begin{tabular}{c}
Amount of hot \\
chocolate sold, y \\
(in liters)
\end{tabular} & 9 & 13 & 8 & 5 & 17 & 15 & 2 \\
\hlineXy & 225 & 39 & 152 & 145 & 136 & 210 & 68 \\
\hlinex
\end{tabular}
Test Scores Which is a better relative position, a score of 80 on a geography test that has a mean of 71 and a standard deviation of 6.5 , or a score of 65 on an accounting test that has a mean of 55 and a standard deviation of 2.5? Part: 0/2□ Part 1 of 2 Find the corresponding z score for each test score. Round z scores to two decimal places.
Geography test z=□
Accounting test z=□
from 1 to 8
Question 40 of 40
This test: 40 point(s) possible
This question: 1 point(s) possible
Submit test Consider a drug that is used to help prevent blood clots in certain patients. In clinical trials, among 5829 patients treated with this drug, 151 developed the adverse reaction of nausea. Use a 0.01 significance level to test the claim that 3% of users develop nausea. Does nausea appear to be a problematic adverse reaction? Identify the null and alternative hypotheses for this test. Choose the correct answer below.
A. H0:p=0.03H1:p>0.03
B. H0:p=0.03H1:p<0.03
C. H0:p=0.03H1:p=0.03
D. H0:p=0.03H1:p=0.03 Identify the test statistic for this hypothesis test.
The test statistic for this hypothesis test is □
(Round to two decimal places as needed.)
Identify the P -value for this hypothesis test.
The P -value for this hypothesis test is □
(Round to three decimal places as needed.)
Dove have obleen ed 10 workers at a production company and have timed how long it takes each to prodace an item. You have been able to mateh the number of items produced with the length wf the work er 's expenence. Assuming that your findings are as displayed in the table below:
\begin{tabular}{|l|c|c|c|c|c|c|c|c|c|c|}
\hline Worker & A & B & C & D & E & F & G & H & I & J \\
\hline Experience(Months) & 2 & 5 & 3 & 8 & 5 & 9 & 12 & 16 & 1 & 6 \\
\hline Time taken (Minutes) & 27 & 26 & 30 & 20 & 22 & 20 & 16 & 15 & 30 & 19 \\
\hline
\end{tabular}
ia) Draw a coatter diagram for the data and comment
[10]
(b) Determine a straight lime equation and estimate how long a worker with 10 months
[10]
expeniance will take to produce an item.
(c) If the compomy would like an item to be produced within 22 mimutes, advise on the
[05]
worker the company it should employ.
[10]
You wish to test the following claim (H1) at a significance level of α=0.05.
Ho:p=0.54H1:p=0.54 You obtain a sample of size n=707 in which there are 374 successful observations.
What is the test statistic for this sample? (Report answer accurate to two decimal places.)
test statistic =□
What is the p-value for this sample? (Report answer accurate to four decimal places.)
p -value = □
The p-value is...
less than (or equal to) α
greater than α This test statistic leáds to a decision to...
reject the null
accept the null
fail to reject the null As such, the final conclusion is that...
There is sufficient evidence to warrant rejection of the claim that the population proportion is not equal to 0.54 .
There is not sufficient evidence to warrant rejection of the claim that the population proportion is not equal to 0.54 .
The sample data support the claim that the population proportion is not equal to 0.54 .
There is not sufficient sample evidence to support the claim that the population proportion is not equal to 0.54 .
A company is doing a hypothesis test on the variation in quality within one supplier. Assume the population is normally distributed. A sample of 14 products was selected. The sample mean was 7 and the sample standard deviation was 1.83 . Test to see if the standard deviation in quality is less than 2.09 by answering the following questions. Assume a significance level of 0.01 .
1) What is the null hypothesis?
H0 : □ ?V □
2) What is the alternative hypothesis?
H1 : □ ?v
□□
3) What is the test statistic value (to 2 decimals)? □
4) What is the p-value (to 4 decimals)? □
5) State your decision.
Accept H0
Do Not Reject H0
Reject H0
6) State your conclusion.
There is not enough evidence that the standard deviation in quality is less than 1.83.
There is not enough evidence that the standard deviation in quality is less than 2.09.
There is enough evidence that the standard deviation in quality is less than 1.83.
There is enough evidence that the standard deviation in quality is less than 2.09.
The random variable (X,Y) has a normal distribution with mean (0,0) and covariance matrix
[1001]□Alox
a) Determine the values of a for which X−aY and X+aY are independent.
b) Determine the mean, covariance matrix, and density of the variable (X−Y,X+Y).
c) What is the distribution of the variable X+3Y+2 ?
0: الويت المبفر 0:18:56
- The next Four (4) questions refer to this situation: Doctors' practices have been categorized as to being Urban, Rural, or Intermediate. The number of doctors who prescribed tetracycline to at least one patient under the age of 8 were recorded for each of these practice :areas. At level of significant 0.01 . The results are Crosstabulation Chi-Square Tests
\begin{tabular}{|l|r|r|r|}
\hline & \multicolumn{1}{|c|}{ Chi-square } & \multicolumn{1}{c|}{ df } & Asymptotic Significance (2-sided) \\
\hline Pearson Chi-Square & 79.2779 & 2 & .000 \\
Likelihood Ratio & 95.463 & 2 & 000 \\
N of Valid Cases & 474 & & \\
\hline
\end{tabular}
a. 0 cells (0.0%) have expected count less than 5 . The minimum expected count is 12.30 .
Specify the Null hypothesis
H0 : Doctors prescribe tetracycline and county type are linearly associated.
0
- Hq : Doctors prescribe tetracycline independent of county type
-
H0 : Doctors prescribe tetracycline and county type are non-linearly associated
0
H0 : Doctors prescribe tetracycline not independent of county type
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19 Annual Miles Driven The average miles driven annually per licensed driver in a certain region of the United States is approximately 12,140 miles. If we assume a fairly mound-shaped distribution with a standard deviation of approximately 3200 miles, find the following: Part: 0/2 Part 1 of 2
(a) Find the z scores. Round z scores to two decimal places. The z score for 14,000 miles is □ . The z score for 9000 miles is □ .
^:૦
Random Variables and Distributions
The sampling distribution of the sample mean
Shaykhah
ian plays a game when he exercises. He chooses a marble from a bag of three marbles: one is red, one is blue, and one is
Español
green. Based on the marble he chooses, he completes a certain number of push-ups, as shown below.
\begin{tabular}{|c|c|}
\hline Marble & Number of push-ups \\
\hline red & 7 \\
\hline blue & 8 \\
\hline green & 8 \\
\hline
\end{tabular} Consider choosing a marble like sampling from a population. (The population mean of the number of push-ups is μ=7.67 and the population standard deviation is σ=0.47.)
(a) Suppose a sample of size 2 is randomly selected from the population, with replacement, as follows. One marble is randomly chosen, the number of push-ups is completed, and the marble is put back into the bag. Then for a second time a marble is randomly chosen and the number of push-ups is completed. There are 9 possible samples. The numbers of push-ups for several of the possible samples have been listed in the table below. Enter the numbers of push-ups for the remaining possible samples. When you are done, select "Compute". In the "Sample mean, xˉ " column, you will then see the sample mean of the numbers of push-ups for each sample, along with the mean and standard deviation of all the column's values.
\begin{tabular}{|c|c|c|l|}
\hline Index & Sample & \begin{tabular}{c}
Numbers \\
of push- \\
ups
\end{tabular} & \\
\hline 1 & red, red & 7,7 & \\
\hline 2 & red, blue & □,□ & \\
\hline 3 & red, green & 7,8 & \\
\hline 4 & blue, red & 8,7 & \\
\hline 5 & blue, blue & 8,8 & \\
\hline 6 & blue, green & □,□ & \\
\hline 7 & green, red & 8,7 & \\
\hline 8 & green, blue & 8,8 & \\
\hline 9 & green, green & □,□ & \\
\hline
\end{tabular}
(b) Use the table from part (a) to find μxˉ (the mean of the sampling distribution of the sample mean) and σxˉ (the standard deviation of the sampling distribution of the sample mean). Write your answers to two decimal places.
μxˉ=σxˉ=□
(c) Graph the frequency histograms for the population distribution and the sampling distribution of the sample mean. Population distribution
Sampling distribution of the sample mean
Frequency
Frequency
Check
(a) A botanist at a nursery wants to inspect the health of the plants at the nursery. Which of the following best describes a stratified sample of plants?
The botanist forms groups of 8 plants based on the heights of the plants. Then, he randomly chooses 7 groups and selects all of the plants in these groups. The botanist forms 7 groups of plants based on the ages of the plants (in months). Then, he selects 8 plants at random from each group.
The botanist assigns each plant a different number. Using a random number table, he draws 56 of those numbers at random. Then, he selects the plants assigned to the drawn numbers. Every set of 56 plants is equally likely to be drawn using the random number table,
(b) A chemist at a pharmaceutical company wants to test the quality of a new batch of microscopes. Which of the following best describes a systematic sample of microscopes? The chemist forms 5 groups of microscopes based on the prices of the microscopes. Then, he selects 18 microscopes at random from each group. The microscopes in the first shipment that was received are easily accessible. So, he selects all 90 of the microscopes in this shipment.
The chemist takes a list of the microscopes and selects every 5th microscope until 90 microscopes are selected.
(c) A facilities supervisor at a sports stadium wants to rate the condition of the seats at the stadium. Which of the following best describes a random sample of seats?
The supervisor uses a computer program to draw 64 seats at random and selects these seats. Every set of 64 seats is equally likely to be drawn by the computer program.
The supervisor takes a list of the seats and selects every 4th seat until 64 seats are selected.
The supervisor forms groups of 8 seats based on the sections the seats are in. Then, she selects all of the seats in 8 randomly chosen groups.
The below scenario describes a real-world or business application that utilizes statistical analysis to help resolve a business problem: increasing efficiency by decreasing processing time. Prepare an analysis by completing five steps of the hypothesis testing with one sample. The report should be a minimum of 5 pages in length. Last week, your manager asked you to analyze staffing needs for the Foreclosure Department. She was so impressed, and she wants you to create another report for her. Her intention is to decrease the processing time per document. Based on last week's report, the average number of processed documents per hour was 15.11 , with a standard deviation of 2.666 . That is, one document was reviewed in 238.25 seconds. To be objective as much as possible, the manager spoke with an employee whose average was exactly 15 documents per hour. The employee claimed that if she was given a larger monitor, the processing time would be shorter. They conducted an experiment with a large monitor and measured processing time. After reviewing 20 documents, the calculated average processing time per document was 190.58 seconds. The manager believes that a bigger monitor helped reduce the processing time for reviewing foreclosure documents. Conduct a hypothesis test using a 95\% confidence level, which means that significance level a=0.05. Use the 5-step process, and explain each term or concept mentioned in each section in the following.
Step 1: Set Up Null and Alternative Hypotheses
Based on the request description, explain if a one-tailed or two-tailed test is needed. If a one-tailed test is needed, is it a left or right-tailed test? Please explain why one alternative is better than the other. State both of the following hypotheses:
- Null hypothesis
- Alternative hypothesis You will need the following information to progress to Step 2:
- Standard deviation: Explain what standard deviation is. Locate the calculated standard deviation in the assignment description, and enter here.
- Random variable: Explain what a random variable is. Locate it in the assignment description, and enter here.
Claim: Fewer than 8.4% of homes have only a landline telephone and no wireless phone. Sample data: A survey by the National Center for Health Statistics showed that among 12,653 homes 5.78% had landline phones without wireless phones. Complete parts (a) and (b).
a. Express the original claim in symbolic form. Let the parameter represent a value with respect to homes that have only a landline telephone and no wireless phone.
□□□
(Type an integer or a decimal. Do not round.)
Claim: The mean systolic blood pressure of all healthy adults is less than 125 mm Hg . Sample data: For 250 healthy adults, the mean systolic blood pressure level is 121.77 mm Hg and the standard deviation is 15.81 mm Hg . Complete parts (a) and (b).
a. Express the original claim in symbolic form. Let the parameter represent a value with respect to systolic blood pressure of a healthy adult.
□□□
(Type an integer or a decimal. Do not round.)
1. Construct a scatter diagram of the two variables, placing GNP per capita (in $1000 s) on the X -axis and % willing to pay more for environmental protection on the Y -axis. 2. The correlation coefficient is .365 . What does this tell you about the relationship between the two variables? 3. The regression equation for this data provides us with the following results:
Y=49.19+0.59XP<.01 Interpret this equation. What do the intercept and slope tell you about the relationship between the two variables? What else can you report about these results?
pueblo was occupied around 1298 A.D. (based on evidence from potsherds and stone tools). The following data give trem-ring dates (A.D.) from adjacent archaeological sites:
\begin{tabular}{|l|l|l|l|l|l|l|l|l|l|}
\hline 1196 & 1274 & 1275 & 1282 & 1282 & 1278 & 1279 & 1323 & 1324 & 1237 \\
\hline
\end{tabular}
§ USE SALT
(a) Use a calculator with sample mean and standard deviation keys to find xˉ and s. (Write your standard deviation in years and round it to four decimal place.)
xˉ=□X A.D. s= Enter an exact number yr 1298 A.D.? Use a 1% level of significance.
(i) What is the level of significance?
0.01 State the null and alternate hypotheses. (Enter != for = as needed.)
H0:μ=1298H1:μ!=1298
(ii) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.
We'll use the standard normal, since we assume that x has a normal distribution and σ is unknown.
We'll use the standard normal, since we assume that x has a normal distribution and σ is known.
We'll use the Student's t, since we assume that x has a normal distribution and σ is unknown.
We'll use the Student's t, since we assume that x has a normal distribution and σ is known. Compute the appropriate sampling distribution value of the sample test statistic. (Round your answer to two decimal places.)
□
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(d): Your answer is incorrect. The records show that the lifetimes of electric bulbs manufactured in the past by BIG Corporation have a mean of 9790 hours and a standard deviation of 124 . The corporation claims that the current standard deviation, σ, is less than 124 following some adjustments in its production unit. A random sample of 27 bulbs from the current production lot is examined by the corporation. The sample has a mean lifetime of 9795 hours, with a standard deviation of 90 . Assume that the lifetimes of the recently manufactured bulbs are approximately normally distributed. Is there enough evidence to conclude, at the 0.10 level of significance, that the corporation's claim is valid? Perform a one-tailed test. Then complete the parts below.
Carry your intermediate computations to three or more decimal places. (If necessary, consult a list of formulas.)
(a) State the null hypothesis H0 and the alternative hypothesis H1.
H0:σ=124H1:σ<124
(b) Determine the type of test statistic to use. Chi-square
Degrees of freedom: 26
(c) Find the value of the test statistic. (Round to three or more decimal places.)
13.698
(d) Find the critical value. (Round to three or more decimal places.)
17.708
(e) Can we support the claim that the current standard deviation of lifetimes of electric bulbs manufactured by the corporation is less than 124 ?
Yes No
Explanation
Recheck
Question: Convergence in Probability
Let X1,X2,… be a sequence of independent and identically distributed (i.i.d.) random variables, where each Xi has the following probability distribution:
P(Xi=0)=21,P(Xi=1)=21.
1 Define the sample mean Xˉn as:
Xˉn=n1i=1∑nXi. We want to analyze the behavior of Xˉn as n→∞.
(a) Show that E[Xi]=21 and Var(Xi)=41.
(b) Using the weak law of large numbers (WLLN), show that XˉnP21 as n→∞. That is, prove that Xˉn converges to 21 in probability.
(c) For a sequence Y1,Y2,… of independent random variables where P(Yi= 1) =1−i1 and P(Yi=0)=i1, determine whether Yn converges in probability to 1 as n→∞. Justify your answer using the definition of convergence in probability.
Suppose that 3 adults have been tested for COVID-19. Assume that the success event is that the individual's test is positive. Also, consider the following snippet from MegaStat output: Binomial distribution
?0.351np
\begin{tabular}{rr}
X & P(X) \\
\hline 0 & 0.273359 \\
1 & ? \\
2 & 0.239872 \\
3 & 0.043244 \\
\hline & 1.00000
\end{tabular}
? expected value
? variance
? standard deviation 17. The mean (μ) is equal to
A) 1.053
B) 0.683397
C) 0.826678
D) 1.947 18. The standard deviation (σ) is equal to
A) 0.826678
B) 1.947
C) 1.053
D) 0.683397 19. The probability that at least one adult are tested positive for COVID-19 is equal to ...
A) 0.956756
B) 0.273359
C) 0.726641
D) 0.716884 20. The probability that less than one adult are tested positive for COVID-19 is equal to ...
A) 0.273359
B) 0.726641
C) 0.716884
D) 0.283116 21. The probability of failure is equal to
A) 0
B) 1
C) 0.649
D) 0.351 22. The average number of pounds of meat that a person consumes per year is 94.5 kg . Assume that the standard deviation is 8.5 kg , and the distribution is approximately normal. If a sample of 75 individuals is selected. What is the probability that the mean of the sample will be at most 97.5 kg per year? Note that: P(X>97.5)=0.362066 and P(Xˉ>97.5)=0.001119.
A) 0.001119
B) 0.637934
C) 0.998881
D) 0.362066 Use the following to answer questions 23-25:
In a study about obesity, suppose that the BMI follows the normal distribution with mean equals to 21.03. Consider the following MegaStat output:
\begin{tabular}{rcrrrr}
P(lower) & P(upper) & z & mean & std.dev \\
0.038764 & & -1.765217 & 19 & ? & ? \\
0.00421 & 0.814781 & -0.895652 & 20 & ? & ? \\
& & -2.634783 & 18 & ? & ? \\
0.995097 & 0.199481 & 0.843478 & 22 & ? & ?
\end{tabular}