Question 1

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

Accepted Answer

When the alternative hypothesi

Question 2

Use the following information to answer questions (1) - (4). 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
-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?

Accepted Answer

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

Question 3

Use the following information to answer questions (1) - (5). Feature movie lengths (in hours) were measured for all movies shown in the past year in the U.S. The mean length of all feature length movies shown was 1.80 hours with a standard deviation of 0.15 hours. Suppose the length of a random sample of 20 movies was recorded from all movies released this year. The mean length of the feature length movies was found to be 1.72 hours with a standard
deviation of 0.18 hours.
-Suppose we were to make a histogram of the feature length movie times of all movies in the past year. The histogram would be a display of which of the following?

Accepted Answer

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

Question 4

Which of the following statements is true about the t-distribution?

Accepted Answer

A) For small sample sizes, the t-distribution has the same properties as the normal curve. 
B) For large sample sizes, the t-distribution has the same properties as the normal curve. 
C) Like the Normal distribution, the t-distribution is symmetric for small n. 
D) Since population standard deviation is usually unknown, the standard error uses the sample standard deviation to estimate population standard deviation. 
A) For small sample sizes, the t-distribution has the same properties as the normal curve. 
B) For large sample sizes, the t-distribution has the same properties as the normal curve. 
C) Like the Normal distribution, the t-distribution is symmetric for small n. 
D) Since population standard deviation is usually unknown, the standard error uses the sample standard deviation to estimate population standard deviation.

Question 5

Use the following information to answer questions (11)-(13). According to the website www.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 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. 
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) 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. 
D) All of the above describe conditions for a valid confidence interval. 
A) 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. 
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) 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. 
D) All of the above describe conditions for a valid confidence interval.

Question 6

Which of the following is a true statement about the Central Limit Theorem for sample means?

Accepted Answer

A) The Normal distribution is a good approximation to the sampling distribution. 
B) If conditions are met, the mean of the sampling distribution is equal to the population mean. 
C) The Central Limit Theorem helps us find probabilities for sample means when those means are based on a random sample from a population. 
D) All of the following statements are true about the Central Limit Theorem for sample means. 
A) The Normal distribution is a good approximation to the sampling distribution. 
B) If conditions are met, the mean of the sampling distribution is equal to the population mean. 
C) The Central Limit Theorem helps us find probabilities for sample means when those means are based on a random sample from a population. 
D) All of the following statements are true about the Central Limit Theorem for sample means.

Question 7

Use the following information to answer questions (12)-(15). Many couples believe that it is getting too expensive to host an "average" wedding in the United States. According to a statistics study in the U.S., the average cost of a wedding in the U.S. in 2014 was $25,200. Recently, in a random sample of 35 weddings in the U.S. it was found that the average cost of a wedding was $24,224 with a standard deviation of $2,210.
-For this description, which of the following does not describe a required condition for a valid confidence interval based on the sample results?

Accepted Answer

A) 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. 
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 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. 
D) The sample size of 35 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 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. 
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 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. 
D) The sample size of 35 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 8

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

Accepted Answer

A) are dependent 
B) are independent 
C) follow a normal distribution 
D) are not a type that can be determined 
A) are dependent 
B) are independent 
C) follow a normal distribution 
D) are not a type that can be determined

Question 9

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.

Accepted Answer

A)  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. 
B)  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. 
C)  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. 
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. 
A)  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. 
B)  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. 
C)  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. 
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 10

Use the following information to answer questions (11)-(13). According to the website 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 11

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.

Accepted Answer

The answer of The weights at birth of five randomly...

Question 12

Use the following information to answer questions (12)-(15). Many couples believe that it is getting too expensive to host an "average" wedding in the United States. According to a statistics study in the U.S., the average cost of a wedding in the U.S. in 2014 was $25,200. Recently, in a random sample of 35 weddings in the U.S. it was found that the average cost of a wedding was $24,224 with a standard deviation of $2,210.
-If a 95% confidence interval for the mean for the wedding sample is ($23465, $24983), does this mean that the sample results are significantly different from the claimed value for the mean of $25,200?

Accepted Answer

A) Since the claimed population mean is outside of the 95% confidence interval, we conclude that the sample results are significantly different. 
B) Since the claimed population mean is outside of the 95% confidence interval, we conclude that there is a 95% chance that the sample results are significantly different. 
C) Since the accepted population average is outside of the 95% confidence interval, we conclude that there is a 5% chance that the sample results are significantly different. 
D) Since the accepted population average is outside of the 95% confidence interval, we conclude that the sample results are not significantly different. 
A) Since the claimed population mean is outside of the 95% confidence interval, we conclude that the sample results are significantly different. 
B) Since the claimed population mean is outside of the 95% confidence interval, we conclude that there is a 95% chance that the sample results are significantly different. 
C) Since the accepted population average is outside of the 95% confidence interval, we conclude that there is a 5% chance that the sample results are significantly different. 
D) Since the accepted population average is outside of the 95% confidence interval, we conclude that the sample results are not significantly different.

Question 13

Use the following information to answer questions (12)-(15). Many couples believe that it is getting too expensive to host an "average" wedding in the United States. According to a statistics study in the U.S., the average cost of a wedding in the U.S. in 2014 was $25,200. Recently, in a random sample of 35 weddings in the U.S. it was found that the average cost of a wedding was $24,224 with a standard deviation of $2,210.
-Which is the best interpretation of a 95% confidence interval for the sample mean.?

Accepted Answer

A) The 95% confidence interval means that we are 95% confident that the sample mean is between the low and high interval values. 
B) The 95% confidence interval means that there is a 95% probability that the population mean is between the low and high interval values. 
C) The 95% confidence interval means that we are 95% confident that the population mean is between the low and high interval values. 
D) The 95% confidence interval means that there is a 95% probability that the sample mean is between the low and high interval values. 
A) The 95% confidence interval means that we are 95% confident that the sample mean is between the low and high interval values. 
B) The 95% confidence interval means that there is a 95% probability that the population mean is between the low and high interval values. 
C) The 95% confidence interval means that we are 95% confident that the population mean is between the low and high interval values. 
D) The 95% confidence interval means that there is a 95% probability that the sample mean is between the low and high interval values.

Question 14

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 15

Use the following information to answer questions (1) - (4). 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)  
B)  
C)  
D)

Accepted Answer

The answer of 
  
A)  
B)  
C)...

Question 17

When the mean of the sampling distribution is the same value as the population parameter, we can say that the statistic is

Accepted Answer

A) a representation of an unbiased parameter. 
B) the standard error. 
C) an unbiased estimator. 
D) unlimited. 
A) a representation of an unbiased parameter. 
B) the standard error. 
C) an unbiased estimator. 
D) unlimited.

Question 18

Use the following information to answer questions (1) - (5). Feature movie lengths (in hours) were measured for all movies shown in the past year in the U.S. The mean length of all feature length movies shown was 1.80 hours with a standard deviation of 0.15 hours. Suppose the length of a random sample of 20 movies was recorded from all movies released this year. The mean length of the feature length movies was found to be 1.72 hours with a standard
deviation of 0.18 hours.
-Suppose the process of taking random samples of size 20 is repeated 200 times and a histogram of the 200 sample means is created. The histogram would be a display of which of the following?

Accepted Answer

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

Question 19

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.

Accepted Answer

The answer of Suppose that a major league baseball game...

Question 20

[Objective: Conduct a hypothesis test on two independent samples] 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. A researcher tested his claim using the following summary statistics:
 
Assume that all conditions for testing have been met.  
; At the 1% significance level, state your decision regarding the null hypothesis and your conclusion about the original claim.

Accepted Answer

A)  Fail to reject the null hypothesis; there is not strong enough evidence to suggest that athletic women are more flexible, on average, than non-athletic women. 
B)  Reject the null hypothesis; there is strong evidence to suggest that athletic women are more flexible, on average, than non-athletic women. 
C)  Reject the null hypothesis; there is strong evidence to suggest that non-athletic women are more flexible, on average, than athletic women. 
D)  Fail to reject the null hypothesis; there is strong evidence to suggest that non-athletic women are more flexible, on average, than athletic women. 
A)  Fail to reject the null hypothesis; there is not strong enough evidence to suggest that athletic women are more flexible, on average, than non-athletic women. 
B)  Reject the null hypothesis; there is strong evidence to suggest that athletic women are more flexible, on average, than non-athletic women. 
C)  Reject the null hypothesis; there is strong evidence to suggest that non-athletic women are more flexible, on average, than athletic women. 
D)  Fail to reject the null hypothesis; there is strong evidence to suggest that non-athletic women are more flexible, on average, than athletic women.

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

Which of the following statements is true about the t-distribution?

Which of the following is a true statement about the Central Limit Theorem for sample means?

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

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

A) B) C) D)

When the mean of the sampling distribution is the same value as the population parameter, we can say that the statistic is

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

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Exam 9: Inferring Population Means

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

Which of the following statements is true about the t-distribution?

Which of the following is a true statement about the Central Limit Theorem for sample means?

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

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

A) B) C) D)

When the mean of the sampling distribution is the same value as the population parameter, we can say that the statistic is

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