Question 1

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

Accepted Answer

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. 
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 2

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.

Accepted Answer

H₀: µ₁= µ₂and H_a: µ₁× µ₂; t = - 3.063; p = 0.0

Question 3

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.

Accepted Answer

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. 
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 4

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 Ha: µ > $5.25
  At the 5% significance level, choose the statement that contains the correct conclusion regarding the hypothesis and the original claim.

Accepted Answer

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. 
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 5

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

Accepted Answer

When many samples of size n are taken fr

Question 6

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.

Accepted Answer

H₀: µ = 400 and H_a: µ > 400; t =

Question 7

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.

Accepted Answer

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

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?

Accepted Answer

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

Question 9

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.

Accepted Answer

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

Question 10

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?

Accepted Answer

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. 
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 11

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?

Accepted Answer

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. 
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.

Question 12

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.

Accepted Answer

A confidence interval does not describe

Question 13

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.

Accepted Answer

The confidence interval provid

Question 14

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.

Accepted Answer

SE = 0.22/

Question 15

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.

Accepted Answer

This is a parameter. It is cal

Question 16

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.

Accepted Answer

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. 
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 17

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 .

Accepted Answer

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

Question 18

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.

Accepted Answer

The distribution will be appro

Question 19

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

Accepted Answer

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. 
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 20

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

Accepted Answer

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. 
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.

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

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

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

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

Introduction to Data

Picturing Variation With Graphs

Numerical Summaries of Center and Variation

Regression Analysis: Exploring Associations Between Variables

Modeling Variation With Probability

Modeling Random Events: the Normal and Binomial Models

Survey Sampling and Inference

Hypothesis Testing for Population Proportions

Associations Between Categorical Variables

Multiple Comparisons and Analysis of Variance

Experimental Design: Controlling Variation

Inference Without Normality

Inference for Regression

Filters

Exam 9: Inferring Population Means

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

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

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

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

Introduction to Data

Picturing Variation With Graphs

Numerical Summaries of Center and Variation

Regression Analysis: Exploring Associations Between Variables

Modeling Variation With Probability

Modeling Random Events: the Normal and Binomial Models

Survey Sampling and Inference

Hypothesis Testing for Population Proportions

Associations Between Categorical Variables

Multiple Comparisons and Analysis of Variance

Experimental Design: Controlling Variation

Inference Without Normality

Inference for Regression

Filters