Deck 9: Inferring Population Means

Question 1

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?

A)The sample distribution must be normally distributed in order to have a valid confidence interval. The problem does not describe the distribution of the sample, so this condition is not met.
B)The sample observations are independent because knowledge about the cost of any one wedding tells us nothing about the cost of any other wedding in the sample.
C)The description states that the sample was randomly selected, so we can assume that the condition which states that the data must represent a random sample is satisfied.
D)The sample size of 40 is large enough that knowledge about the population distribution is not necessary and the condition that the population be normally distributed or sample size be larger than 25 is satisfied.

Answer 1

The sample distribution must be normally distributed in order to have a valid confidence interval. The problem does not describe the distribution of the sample, so this condition is not met.

Question 2

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.

A)z = 1.946; p = 0.974; Fail to reject the null hypothesis; there is not strong evidence to suggest that the highlighters last less than 14 hours.
B)z = 1.946; p = 0.029; Reject the null hypothesis; there is strong evidence to suggest that the highlighters last less than 14 hours.
C)t = - 1.946; p = 0.029; Fail to reject the null hypothesis; there is not strong evidence to suggest that the highlighters last less than 14 hours.
D)t = - 1.946; p = 0.029; Reject the null hypothesis; there is strong evidence to suggest that the highlighters last less than 14 hours.

Answer 2

t = - 1.946; p = 0.029; Reject the null hypothesis; there is strong evidence to suggest that the highlighters last less than 14 hours.

Question 3

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.

A)t = - 1.623; p = 0.054; Reject the null hypothesis; there is strong evidence to suggest that athletic women are more flexible than non- athletic women.
B)t = - 1.623; p = 0.108; Reject the null hypothesis; there is strong evidence to suggest that athletic women are more flexible than non- athletic women.
C)t =1.623; p = 0.108; Reject the null hypothesis; there is not strong evidence to suggest that athletic women are more flexible than non- athletic women.
D)t =1.623; p = 0.054; Fail to reject the null hypothesis; there is not strong evidence to suggest that athletic women are more flexible than non- athletic women.

Answer 3

t =1.623; p = 0.054; Fail to reject the null hypothesis; there is not strong evidence to suggest that athletic women are more flexible than non- athletic women.

Question 4

Which of the following statements is not true about the t- distribution?

A)Like the normal distribution, the t- distribution is symmetric and unimodal.
B)The t- distribution is generally bell- shaped, as sample size increases the shape of the t- distribution gets closer to the shape of the normal distribution.
C)Since population standard deviation is usually unknown, the standard error uses the sample standard deviation to estimate population standard deviation. The formula is SEest = s/ n.
D)All of these statements about the t- distribution are true.

Question 5

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?

A)distribution of a sample
B)sampling distribution of means
C)population distribution

Question 6

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.

A)0.055
B)0.046
C)0.250
D)0.300

Question 7

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.

A)0.250
B)0.046
C)0.055
D)0.300

Question 8

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?

A)population distribution
B)sampling distribution of means
C)distribution of a sample

Question 9

Choose the statement that best describes what is meant when we say that the sample mean is unbiased when estimating the population mean.

A)The standard deviation of the sampling distribution (also called the standard error)and the population standard deviation are equal.
B)On average, the sample mean is the same as the population mean.
C)The sample mean will always equal the population mean.
D)None of these.

Question 10

The college GPA's of identical twins are compared to see whether the means are different.

A)Independent
B)Dependent

Question 11

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.

A)110.0 ± 8.5 pounds
B)111.0 ± 8.5 pounds
C)111.5 ± 9.0 pounds
D)There is not enough information given to calculate the confidence interval.

Question 12

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?

A)The sample size of 40 is large enough that knowledge about the population distribution is not necessary and the condition that the population be normally distributed or sample size be larger than 25 is satisfied.
B)The sample observations are independent because knowledge about the cost of flowers for any one wedding tells us nothing about the cost of flowers for any other wedding in the sample.
C)All of these describe conditions for a valid confidence interval.
D)The description states that the sample was randomly selected, so we can assume that the condition which states that the data must represent a random sample is satisfied.

Question 13

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?

A)Yes
B)No

Question 14

Choose the statement that is the best interpretation of the confidence interval.

A)In about 95% of all samples of 40 U.S. weddings, the resulting confidence interval will contain the mean cost of all weddings in the U.S.
B)That probability that a U.S. wedding will cost more than $24,152 is less than 3%.
C)We are extremely confident that the mean cost of a U.S. wedding is between $22,296 and $24,152.

Question 15

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.

A)0.068
B)This probability cannot be determined because we do not know the distribution of the population.
C)0.494
D)0.006

Question 16

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.

A)z = 9.583; p = 0.000+; Reject the null hypothesis; there is strong evidence to suggest that the highlighters last longer than 14 hours.
B)t = 2.635; p = 0.006; Reject the null hypothesis; there is strong evidence to suggest that the highlighters last longer than 14 hours.
C)z = 9.583; p = 0.000+; Fail to reject the null hypothesis; there is not strong evidence to suggest that the highlighters last longer than 14 hours.
D)t = 2.635; p = 0.006; Fail to reject the null hypothesis; there is not strong evidence to suggest that the highlighters last longer than 14 hours.

Question 17

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?

A)No
B)Yes

Question 18

The reading level of a random sample of men and a random sample of women are measured. Researchers want know whether women typically read at a higher level than men.

A)Independent
B)Dependent

Question 19

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.

A)H0: µ1 = µ2, Ha: µ1 × µ2; p = 0.008; Fail to reject the null hypothesis; there is not strong evidence to suggest that exposure to classical music improved mood rating.
B)H0: µdifference = 0, Ha: µdifference < 0; p = 0.008; Reject the null hypothesis; there is strong evidence to suggest that exposure to classical music improved mood rating.
C)H0: µ1 = µ2, Ha: µ1 < µ2; p = 0.077; Fail to reject the null hypothesis; there is not strong evidence to suggest that exposure to classical music improved mood rating.
D)H0: µdifference = 0, Ha: µdifference > 0; p = 0.922; Fail to reject the null hypothesis; there is not strong evidence to suggest that exposure to classical music improved mood rating.

Question 20

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.

A)384.0 ± 68.0 pounds
B)There is not enough information given to calculate the confidence interval.
C)418.0 ± 34.0 pounds
D)418.0 ± 34.5 pounds

Question 21

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. H₀: 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.

A)Fail to reject the null hypothesis; there is sufficient evidence to support the claim that the average cost of eating at home has increased since 2009.
B)Reject the null hypothesis; there is sufficient evidence to support the claim that the average cost of eating at home has increased since 2009.
C)Fail to reject the null hypothesis; there is not sufficient evidence to support the claim that the average cost of eating at home has increased since 2009.
D)Reject the null hypothesis; there is not sufficient evidence to support the claim that the average cost of eating at home has increased since 2009.

Question 22

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.

A)0.421
B)0.079
C)This probability cannot be determined because we do not know the distribution of the population.
D)0.579

Question 23

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
B)unbiased estimators
C)statistics
D)parameters

Question 24

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.

A)In about 95% of all samples of size 40, the resulting confidence interval will contain the mean cost of flowers at weddings.
B)We are extremely confident that the mean cost of flowers at a wedding is between $701 and $767.
C)That probability that flowers at a wedding will cost less than $767 is nearly 100%.
D)That probability that the flowers at a wedding will cost more than $698 is greater than 5%.

Question 25

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.

A)0.325
B)0.488
C)0.012
D)0.175

Question 26

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.

A)When the alternative hypothesis is two- tailed.
B)When the null hypothesis contains a population parameter that is equal to zero.
C)Both (a)and (b).
D)Neither (a)nor (b). The confidence interval cannot yield results that are the same as the hypothesis test.

Question 27

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?

A)The histogram will be roughly bell- shaped.
B)The histogram will be unimodal.
C)The histogram will be roughly symmetrical.
D)All of these statements are true.

Question 28

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?

A)distribution of a sample
B)sampling distribution of means
C)population distribution

Question 29

Choose the statement that describes a situation where a confidence interval and a hypothesis test will yield the same results.

A)When the alternative hypothesis is two- tailed.
B)When the null hypothesis contains a population parameter that is equal to zero.
C)Both (a)and (b).
D)Neither (a)nor (b). The confidence interval cannot yield results that are the same as the hypothesis test.

Question 30

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.

A)0.345
B)0.477
C)0.023
D)0.155

Question 31

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 .

A)estimates
B)unbiased estimators
C)statistics
D)parameters

Question 32

Which of the following is not a true statement about the Central Limit Theorem for sample means?

A)The Central Limit Theorem helps us find probabilities for sample means when those means are based on a random sample from a population.
B)If the sample size is large, it doesn't matter what the distribution of the population it was drawn from is, the normal distribution can still be used to perform statistical inference.
C)If conditions are met, the mean of the sampling distribution is equal to the population mean.
D)All of these statements are true about the Central Limit Theorem for sample means.

Question 33

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.
H₀: µ = $7.15 H_a: µ < $7.15
Choose the statement that contains the correct conclusion regarding the hypothesis and the original claim.

A)Reject the null hypothesis; there is not sufficient evidence to support the claim that the average cost of eating away from home has decreased since 2009.
B)Fail to reject the null hypothesis; there is sufficient evidence to support the claim that the average cost of eating away from home has decreased since 2009.
C)Fail to reject the null hypothesis; there is not sufficient evidence to support the claim that the average cost of eating away from home has decreased since 2009.
D)Reject the null hypothesis; there is sufficient evidence to support the claim that the average cost of eating away from home has decreased since 2009.

Question 34

Which of the following statements is not true about the t- distribution?

A)Like the normal distribution, the t- distribution is symmetric and unimodal.
B)For small sample sizes, the t- distribution has all the same properties of the normal curve.
C)Since population standard deviation is usually unknown, the standard error uses the sample standard deviation to estimate population standard deviation. The formula is SEest = s/ n.
D)All of these statements about the t- distribution are true.

Question 35

Which of the following is not a true statement about the Central Limit Theorem for sample means?

A)If the sample size is large, it doesn't matter what the distribution of the population it was drawn from is, the normal distribution can still be used to perform statistical inference.
B)The Central Limit Theorem helps us find probabilities for sample means when those means are based on a random sample from a population.
C)If conditions are met, the mean of the sampling distribution is equal to the population mean.
D)All of these statements are true about the Central Limit Theorem for sample means.

Question 36

The weight of King Salmon from Lake Michigan and Lake Superior are measured. Researchers want to know whether Lake Michigan King Salmon weigh less than those from Lake Superior.

A)Independent
B)Dependent

Question 37

Choose the statement that best describes what is meant when we say that the sample mean is unbiased when estimating the population mean.

A)The standard deviation of the sampling distribution (also called the standard error)and the population standard deviation are equal.
B)The sample mean will always equal the population mean.
C)On average, the sample mean is the same as the population mean.
D)None of these.

Question 38

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.

A)H0: µdifference = 0, Ha: µdifference > 0; p = 0.154; Fail to reject the null hypothesis; there is not strong evidence to suggest that exposure to classic rock music decreased mood rating.
B)H0: µdifference = 0, Ha: µdifference > 0; p = 0.015; Fail to reject the null hypothesis; there is not strong evidence to suggest that exposure to classic rock music decreased mood rating.
C)H0: µdifference = 0, Ha: µdifference > 0; p = 0.154; Reject the null hypothesis; there is strong evidence o suggest that exposure to classic rock music decreased mood rating.
D)H0: µdifference = 0, Ha: µdifference × 0; p = 0.309; Reject the null hypothesis; there is strong evidence to suggest that exposure to classic rock music decreased mood rating.

Question 39

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.

A)t = - 3.270; p = 0.002; Reject the null hypothesis; there is strong evidence to suggest that athletic men are more flexible than non- athletic men.
B)t = 3.270; p = 0.001; Fail to reject the null hypothesis; there is not strong evidence to suggest that athletic men are more flexible than non- athletic men.
C)t = 3.270; p = 0.001; Reject the null hypothesis; there is strong evidence to suggest that athletic men are more flexible than non- athletic men.
D)t = - 3.270; p = 0.002; Reject the null hypothesis; there is not strong evidence to suggest that athletic men are more flexible than non- athletic men.

Question 40

The productivity of manufacturing plant workers is compared before and after the installation of air conditioning.

A)Independent
B)Dependent

Question 41

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.

Question 42

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.

Question 43

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.

Question 44

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.

Question 45

Compare the normal distribution and the t- distribution. How are they similar? How are they different?

Question 46

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.

Question 47

What is the expected finish time for a male participant in the sample of 30? Will the expected mean finish time be the same for any sample of 30 males drawn from the population? Explain.

Question 48

Describe the circumstances under which a confidence interval and hypothesis test yield the same results?

Question 49

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.
H₀: 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?

Question 50

How might the shapes of a population distribution and a sampling distribution look the same? How might they look different?

Question 51

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.

Question 52

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.

Question 53

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.

Question 54

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.

Question 55

Explain what is meant when we say that the sample mean is an unbiased estimator.

Question 56

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.

Question 57

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.

Question 58

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.

Question 59

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.

Question 60

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.