## Introductory Statistics

Statistics

## Quiz 9 :

Inferring Population Means

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Q01 Q01 Q01

A researcher wants to know if mood is affected by music. She conducts a test on a sample of 4 randomly selected adults and measures mood rating before and after being exposed to classical music. Test the hypothesis that mood rating improved after being exposed to classical music. Following are the mood ratings for the four participants: Assume that all conditions for testing have been met. Report the null and alternative hypothesis and p- value. At the 5% significance level, state your decision regarding the null hypothesis and your conclusion about the original claim. Round all values to the nearest thousandth.

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B

Q02 Q02 Q02

The weights at birth of five randomly chosen baby Orca whales were 425, 454, 380, 405, and 426 pounds. Assume the distribution of weights is normally distributed. Find a 95% confidence interval for the mean weight of all baby Orca whales. Use technology for your calculations. Give the confidence interval in the form "estimate ± margin of error." Round to the nearest tenth of a pound.

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C

Q03 Q03 Q03

Suppose a consumer product researcher wanted to find out whether a highlighter lasted less than the manufacturer's claim that their highlighters could write continuously for 14 hours. The researcher tested 40 highlighters and recorded the number of continuous hours each highlighter wrote before drying up. Test the hypothesis that the highlighters wrote for less than 14 continuous hours. Following are the summary statistics: x =13.6 hours, s =1.3 hours
Report the test statistic, p- value, your decision regarding the null hypothesis, and your conclusion about the original claim. Round all values to the nearest thousandth.

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D

Q04 Q04 Q04

Use the following information to answer the question. A sprint duathlon consists of a 5 km run, a 20 km bike ride, followed by another 5 km run. The mean finish time of all participants in a recent large duathlon was 1.67 hours with a standard deviation of 0.25 hours. Suppose a random sample of 30 participants was taken and the mean finishing time was found to be
1.59 hours with a standard deviation of 0.30 hours.
-What is the standard error for the mean finish time of 30 randomly selected participants? Round to the nearest thousandth.

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Q05 Q05 Q05

Suppose a consumer product researcher wanted to find out whether a highlighter lasted longer than the manufacturer's claim that their highlighters could write continuously for 14 hours. The researcher tested 40 highlighters and recorded the number of continuous hours each highlighter wrote before drying up. Test the hypothesis that the highlighters wrote for more than 14 continuous hours. Following are the summary statistics: x =14.5 hours, s =1.2 hours
Report the test statistic, p- value, your decision regarding the null hypothesis. At the 5% significance level, state your conclusion about the original claim. Round all values to the nearest thousandth.

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Q06 Q06 Q06

The weights at birth of five randomly chosen baby giraffes were 111, 115, 120, 103, and 106 pounds. Assume the distribution of weights is normally distributed. Find a 95% confidence interval for the mean weight of all baby giraffes. Use technology for your calculations. Give the confidence interval in the form "estimate ± margin of error." Round to the nearest tenth of a pound.

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Q09 Q09 Q09

Suppose that the average country song length in America is 4.75 minutes with a standard deviation of 1.10 minutes. It is known that song length is not normally distributed. Find the probability that a single randomly selected song from the population will be less than 4.20 minutes. Round to the nearest thousandth.

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Q11 Q11 Q11

Use the following information to answer the question. A sprint duathlon consists of a 5 km run, a 20 km bike ride, followed by another 5 km run. The mean finish time of all participants in a recent large duathlon was 1.67 hours with a standard deviation of 0.25 hours. Suppose a random sample of 30 participants was taken and the mean finishing time was found to be
1.59 hours with a standard deviation of 0.30 hours.
-Suppose we were to make a histogram of the finishing times of all participants in the duathlon. Would the histogram be a display of the population distribution, the distribution of a sample, or the sampling distribution of means?

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Q12 Q12 Q12

Use the following information to answer the question. A sprint duathlon consists of a 5 km run, a 20 km bike ride, followed by another 5 km run. The mean finish time of all participants in a recent large duathlon was 1.67 hours with a standard deviation of 0.25 hours. Suppose a random sample of 30 participants in the 40- 44 age group was taken and the mean finishing time was found to be 1.62 hours with a standard deviation of 0.40 hours.
-What is the standard error for the mean finish time of 30 randomly selected participants in the 40- 44 age group? Round to the nearest thousandth.

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Q13 Q13 Q13

Use the following information to answer the question. According to the website ww.costofwedding.com, the average cost of flowers for a wedding is $698. Recently, in a random sample of 40 weddings in the U.S. it was found that the average cost of the flowers was $734, with a standard deviation of $102. On the basis of this, a 95% confidence interval for the mean cost of flowers for a wedding is $701 to $767.
-For this description, which of the following does not describe a condition for a valid confidence interval?

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Q14 Q14 Q14

Use the following information to answer the question. A sprint duathlon consists of a 5 km run, a 20 km bike ride, followed by another 5 km run. The mean finish time of all participants in a recent large duathlon was 1.67 hours with a standard deviation of 0.25 hours. Suppose a random sample of 30 participants was taken and the mean finishing time was found to be
1.59 hours with a standard deviation of 0.30 hours.
-Suppose the process of taking random samples of size 30 is repeated 200 times and a histogram of the 200 sample means is created. Would the histogram be an approximate display of the population distribution, the distribution of a sample, or the sampling distribution of means?

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Q15 Q15 Q15

A researcher wants to know whether athletic women are more flexible than non- athletic women. For this experiment, a woman who exercised vigorously at least four times per week was considered "athletic." Flexibility is measured in inches on a sit & reach box. Test the researcher's claim using the following summary statistics: Assume that all conditions for testing have been met. Report the test statistic and p- value. At the 1% significance level, state your decision regarding the null hypothesis and your conclusion about the original claim. Round all values to the nearest thousandth.

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Q16 Q16 Q16

Use the following information to answer the question. Many couples believe that it is getting too expensive to host an "average" wedding in the United States. According to the website HYPERLINK "http://www.costofwedding.com/" www.costofwedding.com, the average cost of a wedding in the U.S. in 2009 was $24,066. Recently, in a random sample of 40 weddings in the U.S. it was found that the average cost of a wedding was $23,224, with a standard deviation of $2,903. On the basis of this, a 95% confidence interval for the mean cost of weddings in the U.S. is $22,296 to $24,152.
-For this description, which of the following does not describe a condition for a valid confidence interval?

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Q17 Q17 Q17

Use the following information to answer the question. According to the website ww.costofwedding.com, the average cost of flowers for a wedding is $698. Recently, in a random sample of 40 weddings in the U.S. it was found that the average cost of the flowers was $734, with a standard deviation of $102. On the basis of this, a 95% confidence interval for the mean cost of flowers for a wedding is $701 to $767.
-Does the confidence interval provide evidence that the mean cost of flowers for a wedding has increased?

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Q18 Q18 Q18

Use the following information to answer the question. Many couples believe that it is getting too expensive to host an "average" wedding in the United States. According to the website HYPERLINK "http://www.costofwedding.com/" www.costofwedding.com, the average cost of a wedding in the U.S. in 2009 was $24,066. Recently, in a random sample of 40 weddings in the U.S. it was found that the average cost of a wedding was $23,224, with a standard deviation of $2,903. On the basis of this, a 95% confidence interval for the mean cost of weddings in the U.S. is $22,296 to $24,152.
-Does the confidence interval provide evidence that the mean cost of a wedding has decreased?

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Q21 Q21 Q21

Use the following information to answer the question. A sprint duathlon consists of a 5 km run, a 20 km bike ride, followed by another 5 km run. The mean finish time of all participants in a recent large duathlon was 1.67 hours with a standard deviation of 0.25 hours. Suppose a random sample of 30 participants was taken and the mean finishing time was found to be
1. hours with a standard deviation of 0.30 hours.
-In this example, the numerical values of 1.67 hours and 0.25 hours are .

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Q22 Q22 Q22

Use the following information to answer the question. A sprint duathlon consists of a 5 km run, a 20 km bike ride, followed by another 5 km run. The mean finish time of all participants in a recent large duathlon was 1.67 hours with a standard deviation of 0.25 hours. Suppose a random sample of 30 participants in the 40- 44 age group was taken and the mean finishing time was found to be 1.62 hours with a standard deviation of 0.40 hours.
-In this example, the numerical values of 1.62 hours and 0.40 hours are .
A)estimates

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Q24 Q24 Q24

Use the following information to answer the question. According to the website ww.costofwedding.com, the average cost of flowers for a wedding is $698. Recently, in a random sample of 40 weddings in the U.S. it was found that the average cost of the flowers was $734, with a standard deviation of $102. On the basis of this, a 95% confidence interval for the mean cost of flowers for a wedding is $701 to $767.
-Choose the statement that is the best interpretation of the confidence interval.

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Q25 Q25 Q25

Suppose that the average song length in America is 4 minutes with a standard deviation of 1.25 minutes. It is known that song length is not normally distributed. Find the probability that a single randomly selected song from the population will be longer than 4.25 minutes. Round to the nearest thousandth.

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Q26 Q26 Q26

A researcher wants to know if mood is affected by music. She conducts a test on a sample of 4 randomly selected adults and measures mood rating before and after being exposed to classic rock music. Test the hypothesis that mood rating decreased after being exposed to classic rock music. Following are the mood ratings for the four participants: Assume that all conditions for testing have been met. Report the null and alternative hypothesis and p- value. At the 5% significance level, state your decision regarding the null hypothesis and your conclusion about the original claim. Round all values to the nearest thousandth.

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Q27 Q27 Q27

An economist conducted a hypothesis test to test the claim that the average cost of eating a meal at home increased from 2009 to 2010. The average cost of eating a meal at home in 2009 was $5.25 per person per meal. Assume that all conditions for testing have been met. He used technology to complete the hypothesis test. Following is his null and alternative hypothesis and the output from his graphing calculator. H

_{0}: µ = $5.25 H_{a}: µ > $5.25 At the 5% significance level, choose the statement that contains the correct conclusion regarding the hypothesis and the original claim.Free

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Q29 Q29 Q29

Suppose that the average pop song length in America is 4 minutes with a standard deviation of 1.25 minutes. It is known that song length is not normally distributed. Suppose a sample of 25 songs is taken from the population. What is the approximate probability that the average song length will be less than 3.5 minutes? Round to the nearest thousandth.

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Q32 Q32 Q32

An economist conducted a hypothesis test to test the claim that the average cost of eating a meal away from home decreased from 2009 to 2010. The average cost of eating a meal away from home in 2009 was $7.15 per person per meal. Assume that all
Conditions for testing have been met. He used technology to complete the hypothesis test.
Following is his
Null and alternative hypothesis and the output from his graphing calculator.
H

_{0}: µ = $7.15 H_{a}: µ < $7.15 Choose the statement that contains the correct conclusion regarding the hypothesis and the original claim.Free

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Q34 Q34 Q34

A researcher wants to know whether athletic men are more flexible than non- athletic men. For this experiment, a man who exercised vigorously at least four times per week was considered "athletic." Flexibility is measured in inches on a sit & reach box. Test the researcher's claim using the following summary statistics: Assume that all conditions for testing have been met. Report the test statistic and p- value. At the 5% significance level, state your decision regarding the null hypothesis and your conclusion about the original claim. Round all values to the nearest thousandth.

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Q35 Q35 Q35

Use the following information to answer the question. A sprint duathlon consists of a 5 km run, a 20 km bike ride, followed by another 5 km run. The mean finish time of all participants in a recent large duathlon was 1.67 hours with a standard deviation of 0.25 hours. Suppose a random sample of 30 participants in the 40- 44 age group was taken and the mean finishing time was found to be 1.62 hours with a standard deviation of 0.40 hours.
-Suppose the process of taking random samples of size 30 from the 40- 44 age group is repeated 200 times and a histogram of the 200 sample means is created. Which statement best describes the shape of the histogram?

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Q36 Q36 Q36

Use the following information to answer the question. A sprint duathlon consists of a 5 km run, a 20 km bike ride, followed by another 5 km run. The mean finish time of all participants in a recent large duathlon was 1.67 hours with a standard deviation of 0.25 hours. Suppose a random sample of 30 participants in the 40- 44 age group was taken and the mean finishing time was found to be 1.62 hours with a standard deviation of 0.40 hours.
-Suppose that the average country song length in America is 4.75 minutes with a standard deviation of 1.10 minutes. It is known that song length is not normally distributed. Suppose a sample of 25 songs is taken from the population. What is the approximate probability that the average song length will last more than 5.25 minutes? Round to the nearest thousandth.

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Q39 Q39 Q39

Use the following information to answer the question. A sprint duathlon consists of a 5 km run, a 20 km bike ride, followed by another 5 km run. The mean finish time of all participants in a recent large duathlon was 1.67 hours with a standard deviation of 0.25 hours. Suppose a random sample of 30 participants in the 40- 44 age group was taken and the mean finishing time was found to be 1.62 hours with a standard deviation of 0.40 hours.
-Suppose we were to make a histogram of the finishing times of the 30 participants in the 40- 44 age group. Would the histogram be a display of the population distribution, the distribution of a sample, or the sampling distribution of means?

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Q40 Q40 Q40

Use the following information to answer the question. A sprint duathlon consists of a 5 km run, a 20 km bike ride, followed by another 5 km run. The mean finish time of all participants in a recent large duathlon was 1.67 hours with a standard deviation of 0.25 hours. Suppose a random sample of 30 participants in the 40- 44 age group was taken and the mean finishing time was found to be 1.62 hours with a standard deviation of 0.40 hours.
-Choose the statement that describes a situation where a confidence interval and a hypothesis test will yield the same results.

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Q41 Q41 Q41

Suppose that a major league baseball game has an average length of 2.9 hours with a standard deviation of 0.5 hours. It is known that game length is not normally distributed. Suppose a random sample of 36 games is taken from the population. Sketch the probability distribution and shade in the region that corresponds to the probability. What is the approximate probability that average game length will be greater than 3.1 hours? Round to the nearest thousandth.

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Q42 Q42 Q42

State whether the situation has dependent or independent samples. A researcher wants to know if reaction time is affected by body type of the vehicle being driven. He measures the reaction time of 40 drivers while they drive a compact car then he measures the reaction time while they drive an SUV.

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Q44 Q44 Q44

Suppose that a major league baseball game has an average length of 2.9 hours with a standard deviation of 0.5 hours. It is known that game length is not normally distributed. Suppose a random sample of 36 games is taken from the population. What is the approximate probability that average game length will be greater than 3.15 hours or less than 2.75 hours? Round to the nearest thousandth.

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Q45 Q45 Q45

The weights at birth of five randomly chosen baby hippopotamuses were 75, 99, 107, 82, and 63 pounds. Assume the distribution of weights is normally distributed. Find a 95% confidence interval for the mean weight of all baby hippopotamuses. Use technology for your calculations. Give the confidence interval in the form "estimate ± margin of error." Round to the nearest pound.

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Q46 Q46 Q46

Use the following information to answer the question. According to the website HYPERLINK "http://www.costofwedding.com/" www.costofwedding.com, the average cost of catering a wedding (with an open bar)is $100 per person. Recently, in a random sample of 40 weddings in the U.S. it was found that the average catering cost was $110, with a standard deviation of $12. On the basis of this, a 95% confidence interval for the mean catering cost for a wedding is $106 to $114.
-Verify that the conditions for a valid confidence interval are met.

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Q50 Q50 Q50

Use the following information to answer the question. A sprint duathlon consists of a 5 km run, a 20 km bike ride, followed by another 5 km run. The mean finish time of all male participants in a recent large duathlon was 1.54 hours with a standard deviation of 0.22 hours. The distribution of finish times for males is right- skewed. Suppose that a sample of 30 randomly selected male participants is selected.
-Suppose that the process of drawing samples of size 30 from the population of all male participants is repeated 100 times. If possible, sketch and describe what the sampling distribution of the means will look like and state the approximate mean value of the distribution. Round to the nearest thousandth.

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Q51 Q51 Q51

State whether the situation has dependent or independent samples. A researcher wants to know if reaction time is affected by the gender of the driver. He measures the reaction time of 30 female drivers while they drive a compact car, then he measures the reaction time of 30 male drivers while they drive a compact car.

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Q52 Q52 Q52

A sociologist wants to know whether there is a difference in the mean number of times that men and women in the U.S. check their Smartphone during the day. Test the hypothesis that the mean number of times that men and women in the U.S. check their Smartphone during the day is different. Following are the summary statistics:
Assume that all conditions for testing have been met. Be sure to report the null and alternative hypothesis, test statistic, p- value, your decision regarding the null hypothesis, and your conclusion about the original claim. Round all values to the nearest thousandth.

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Q53 Q53 Q53

The quality engineer at a paint manufacturer conducted a hypothesis test to test the claim that the mean volume of paint cans had changed after an adjustment in the manufacturing process. Mean volume in paint cans before the adjustment was 1.02 gallons. Assume that all conditions for testing have been met. She used technology to complete the hypothesis test. Following is the null and alternative hypothesis and the output from her graphing calculator.
H

_{0}: µ = 1.02 gallons H_{a}: µ × 1.02 gallons Write a statement explaining what her decision regarding the null hypothesis should be and a statement summarizing her conclusion regarding the claim that average volume of paint cans had changed. Has the adjustment in the manufacturing process changed the average volume of paint cans?Free

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Q54 Q54 Q54

Use the following information to answer the question. A sprint duathlon consists of a 5 km run, a 20 km bike ride, followed by another 5 km run. The mean finish time of all male participants in a recent large duathlon was 1.54 hours with a standard deviation of 0.22 hours. The distribution of finish times for males is right- skewed. Suppose that a sample of 30 randomly selected male participants is selected.
-Calculate the standard error for the mean finish time of 30 randomly selected male participants. Show all your work and round to the nearest thousandth.

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Q56 Q56 Q56

Suppose a consumer product researcher wanted to find out whether a printer ink cartridge lasted longer than the manufacturer's claim that their ink cartridges could print 400 pages. The researcher tested 40 ink cartridges and recorded the number of pages that were printed before the ink started to fade. Test the hypothesis that the ink cartridges lasted for more than 400 pages. Following are the summary statistics:
x = 415 pages, s = 30 pages
Be sure to report the null and alternative hypothesis, test statistic, p- value, your decision regarding the null hypothesis, and your conclusion about the original claim. Round all values to the nearest thousandth.

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Q57 Q57 Q57

Use the following information to answer the question. A sprint duathlon consists of a 5 km run, a 20 km bike ride, followed by another 5 km run. The mean finish time of all male participants in a recent large duathlon was 1.54 hours with a standard deviation of 0.22 hours. The distribution of finish times for males is right- skewed. Suppose that a sample of 30 randomly selected male participants is selected.
-Is the number 1.54 a statistic or parameter? Explain.

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Q58 Q58 Q58

Use the following information to answer the question. According to the website HYPERLINK "http://www.costofwedding.com/" www.costofwedding.com, the average cost of catering a wedding (with an open bar)is $100 per person. Recently, in a random sample of 40 weddings in the U.S. it was found that the average catering cost was $110, with a standard deviation of $12. On the basis of this, a 95% confidence interval for the mean catering cost for a wedding is $106 to $114.
-Explain whether the confidence interval provides evidence that the mean catering cost of a wedding has increased.

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Q59 Q59 Q59

A chewing gum manufacturer wants to know whether students score higher on math tests when they are allowed to chew gum during a test. He conducts an experiment with a sample of four randomly selected students and records the test results with gum chewing and without. Test the hypothesis that test scores were higher when students were allowed to chew gum during the test. Following are the test scores for the four participants:
Assume that all conditions for testing have been met. Be sure to report the null and alternative hypothesis, test statistic, p- value, your decision regarding the null hypothesis, and your conclusion about the original claim. Round all values to the nearest thousandth.

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Q60 Q60 Q60

Use the following information to answer the question. According to the website HYPERLINK "http://www.costofwedding.com/" www.costofwedding.com, the average cost of catering a wedding (with an open bar)is $100 per person. Recently, in a random sample of 40 weddings in the U.S. it was found that the average catering cost was $110, with a standard deviation of $12. On the basis of this, a 95% confidence interval for the mean catering cost for a wedding is $106 to $114.
-A popular wedding magazine states in an article on catering costs that "There is a 95% chance that the catering cost of your wedding will be between $106 and $114 per person." Explain what is wrong with this statement and write a better statement that correctly interprets the confidence interval.

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