Ch.3 Full Test Bank Confidence Intervals

Statistics - Unlocking the Power of Data, 3e (Lock)

Chapter 3 Confidence Intervals

3.1 Sampling Distributions

Use the following to answer the questions below:

Identify each of the following as either a parameter or a statistic, and give the correct notation.

1) Correlation between height and armspan (distance from fingertip to fingertip when arms are extended to the sides) for all players on the Chicago Bulls basketball team, using data from all players currently on the team

A) Parameter, ρ

B) Parameter,

C) Statistic,

D) Statistic, ρ

Diff: 2 Type: BI Var: 1

L.O.: 3.1.1

2) Proportion of students at your university that smoke, based on data from your class.

A) Statistic,

B) Parameter, ρ

C) Parameter,

D) Statistic, ρ

Diff: 2 Type: BI Var: 1

L.O.: 3.1.1

3) Correlation between price of a textbook and the number of pages, based on 25 textbooks selected from the bookstore.

A) Statistic, r

B) Parameter, p

C) Parameter, μ

D) Statistic,

Diff: 2 Type: BI Var: 1

L.O.: 3.1.1

4) Average commute time for employees at a small company, based on interviews with all employees.

A) Parameter, μ

B) Statistic, r

C) Parameter, p

D) Statistic,

Diff: 2 Type: BI Var: 1

L.O.: 3.1.1

5) Average gas price in Minnesota, based on prices at randomly selected gas stations throughout the state.

A) Statistic,

B) Statistic, r

C) Parameter, p

D) Parameter, μ

Diff: 2 Type: BI Var: 1

L.O.: 3.1.1

6) Proportion of students at a university that are part-time, based on data on all students enrolled at the university.

A) Parameter, p

B) Statistic, r

C) Parameter, μ

D) Statistic,

Diff: 2 Type: BI Var: 1

L.O.: 3.1.1

7) Briefly explain the distinction between a parameter and a statistic.

Diff: 2 Type: ES Var: 1

L.O.: 3.1.1

Use the following to answer the questions below:

The sampling distribution shows sample proportions from samples of size n = 35.

8) What does one dot on the sampling distribution represent?

Diff: 2 Type: ES Var: 1

L.O.: 3.1.3

9) Estimate the population proportion from the dotplot.

A) 0.56

B) 0.63

C) 0.70

D) 0.91

Diff: 2 Type: BI Var: 1

L.O.: 3.1.4

10) Estimate the standard error of the sample proportions.

A) 0.07

B) 0.63

C) 0.14

D) 0.01

Diff: 2 Type: BI Var: 1

L.O.: 3.1.5

11) Using the sampling distribution, how likely is = 0.65?

A) Reasonably likely to occur from a sample of this size

B) Unusual but might occur occasionally

C) Extremely unlikely to ever occur

Diff: 2 Type: BI Var: 1

L.O.: 3.1.3

12) Using the sampling distribution, how likely is = 0.45?

A) Reasonably likely to occur from a sample of this size

B) Unusual but might occur occasionally

C) Extremely unlikely to ever occur

Diff: 2 Type: BI Var: 1

L.O.: 3.1.3

13) Using the sampling distribution, how likely is = 0.98?

A) Reasonably likely to occur from a sample of this size

B) Unusual but might occur occasionally

C) Extremely unlikely to ever occur

Diff: 2 Type: BI Var: 1

L.O.: 3.1.3

14) If samples of size n = 65 had been used instead of n = 35, which of the following would be true?

A) The sample statistics would be centered at a larger proportion.

B) The sample statistics would be centered at roughly the same proportion.

C) The sample statistics would be centered at a smaller proportion.

Diff: 2 Type: BI Var: 1

L.O.: 3.1.6

15) If samples of size n = 65 had been used instead of n = 35, which of the following would be true?

A) The sample statistics would have more variability.

B) The variability in the sample statistics would be about the same.

C) The sample statistics would have less variability.

Diff: 2 Type: BI Var: 1

L.O.: 3.1.6

Use the following to answer the questions below:

The sampling distribution shows sample means from samples of size n = 50.

16) What does one dot on the sampling distribution represent?

Diff: 2 Type: ES Var: 1

L.O.: 3.1.3

17) Estimate the population mean from the dotplot.

A) 62

B) 63

C) 65

D) 67

Diff: 2 Type: BI Var: 1

L.O.: 3.1.4

18) Estimate the standard error of the sample means.

A) 1

B) 2

C) 3

D) 5

Diff: 2 Type: BI Var: 1

L.O.: 3.1.5

19) Using the sampling distribution, how likely is = 55.6?

A) Reasonably likely to occur from a sample of this size

B) Unusual but might occur occasionally

C) Extremely unlikely to ever occur

Diff: 2 Type: BI Var: 1

L.O.: 3.1.3

20) Using the sampling distribution, how likely is = 64.2?

A) Reasonably likely to occur from a sample of this size

B) Unusual but might occur occasionally

C) Extremely unlikely to ever occur

Diff: 2 Type: BI Var: 1

L.O.: 3.1.3

21) Using the sampling distribution, how likely is = 68.7?

A) Reasonably likely to occur from a sample of this size

B) Unusual but might occur occasionally

C) Extremely unlikely to ever occur

Diff: 2 Type: BI Var: 1

L.O.: 3.1.3

22) If samples of size n = 30 had been used instead of n = 50, which of the following would be true?

A) The sample means would be centered at a larger value.

B) The sample means would be centered at the same value.

C) The sample means would be centered at a smaller value.

Diff: 2 Type: BI Var: 1

L.O.: 3.1.6

23) If samples of size n = 30 had been used instead of n = 50, which of the following would be true?

A) The sample means would have more variability.

B) The variability in the sample statistics would be about the same.

C) The sample means would have less variability.

Diff: 2 Type: BI Var: 1

L.O.: 3.1.6

Use the following to answer the questions below:

In a survey of 7,786 randomly selected adults living in Germany, 5,840 said they exercised for at least 30 minutes three or more times per week.

24) Identify, with the proper notation, the quantity being estimated.

A) p = proportion of German adults who exercise for 30 minutes three or more times per week.

B) = proportion number of German adults who exercise for 30 minutes three or more times per week.

C) p = the number of German adults who exercise for 30 minutes three or more times per week.

D) = the number of German adults who exercise for 30 minutes three or more times per week.

Diff: 2 Type: BI Var: 1

L.O.: 3.1.1

25) Using the correct notation, give the value of the best estimate of the population parameter. Round your answer to two decimal places.

Diff: 2 Type: SA Var: 1

L.O.: 3.1.2

Use the following to answer the questions below:

According to U.S. Census data, 71.6% of Americans are age 21 and over. The provided figure shows possible sampling distributions for the proportion of a sample age 21 and over, for samples of size n = 50, n = 125, and n = 250.

Match the sample sizes (n = 50, n = 125, and n = 250) to their sampling distribution.

26) Sample A: n = ________

Diff: 2 Type: SA Var: 1

L.O.: 3.1.6

27) Sample B: n = ________

Diff: 2 Type: SA Var: 1

L.O.: 3.1.6

28) Sample C: n = ________

Diff: 2 Type: SA Var: 1

L.O.: 3.1.6

Use the following to answer the questions below:

According to ESPN.com, the average number of yards per game for all NFL running backs with at least 50 attempts in the 2011 season was 49 yards/game. A sample of 20 running backs from the 2011 season averaged 46.54 yards/game.

29) Is 49 yards/game a parameter or statistic?

A) Parameter

B) Statistic

Diff: 2 Type: BI Var: 1

L.O.: 3.1.1

30) Is 46.54 yards/game a parameter or statistic?

A) Parameter

B) Statistic

Diff: 2 Type: BI Var: 1

L.O.: 3.1.1

31) Two boxplots are shown. One boxplot corresponds to the yards/game for a random sample of running backs. The other boxplot represents the values in a sampling distribution of 1,000 means of yards/game for samples of size n = 20.

Which boxplot represents the sample? Which boxplot represents the sampling distribution?

A) Boxplot A is the sampling distribution while Boxplot B is a single sample.

B) Boxplot B is the sampling distribution while Boxplot A is a single sample.

Diff: 3 Type: BI Var: 1

L.O.: 3.1.0

3.2 Understanding and Interpreting Confidence Intervals

Use the following to answer the questions below:

A random sample of 200 students shows that 62% of students use the Student Health Center at some point during their time on campus, with a margin of error of ± 4%. Based on this information, identify each of the following as plausible or not for the percent of the entire student body that use the Student Health Center at some point during their time on campus.

1) 50%

A) Plausible

B) Not Plausible

Diff: 2 Type: BI Var: 1

L.O.: 3.2.1;3.2.2

2) 60%

A) Plausible

B) Not Plausible

Diff: 2 Type: BI Var: 1

L.O.: 3.2.1;3.2.2

3) 65%

A) Plausible

B) Not Plausible

Diff: 2 Type: BI Var: 1

L.O.: 3.2.1;3.2.2

4) 72%

A) Plausible

B) Not Plausible

Diff: 2 Type: BI Var: 1

L.O.: 3.2.1;3.2.2

Use the following to answer the questions below:

In a recent Gallup survey of 1,012 randomly selected U.S. adults (age 18 and over), 53% said that they were dissatisfied with the quality of education students receive in kindergarten through grade 12. They also report that the "margin of sampling error is plus or minus 4%."

5) What is the population of interest?

A) U.S. adults (age 18 and over)

B) 1,012 randomly selected U.S. adults

C) U.S. adults dissatisfied with K-12 education

D) U.S. adults satisfied with K-12 education

Diff: 1 Type: BI Var: 1

L.O.: 1.2.1;3.1.0

6) What is the sample being used?

A) 1,012 randomly selected U.S. adults

B) U.S. adults (age 18 and over)

C) U.S. adults dissatisfied with K-12 education

D) U.S. adults satisfied with K-12 education

Diff: 1 Type: BI Var: 1

L.O.: 1.2.1;3.1.0

7) What is the population parameter of interest, and what is the correct notation for this parameter?

A) p = proportion of U.S. adults who are dissatisfied with the quality of education students receive in kindergarten through grade 12

B) = proportion of the sample of 1,012 randomly selected U.S. adults who are dissatisfied = 0.53

C) p = proportion of the sample of 1,012 randomly selected U.S. adults who are dissatisfied = 0.53

D) =proportion of U.S. adults who are dissatisfied with the quality of education students receive in kindergarten through grade 12

Diff: 2 Type: BI Var: 1

L.O.: 3.1.1

8) What is the relevant statistic?

A) = proportion of the sample of 1,012 randomly selected U.S. adults who are dissatisfied = 0.53

B) p = proportion of U.S. adults who are dissatisfied with the quality of education students receive in kindergarten through grade 12

C) p = proportion of the sample of 1,012 randomly selected U.S. adults who are dissatisfied = 0.53

D) = proportion of U.S. adults who are dissatisfied with the quality of education students receive in kindergarten through grade 12

Diff: 2 Type: BI Var: 1

L.O.: 3.1.1

9) Find an interval estimate for the parameter of interest. Interpret it in terms of dissatisfaction in the quality of education students receive. Use two decimal places in your answer.

A) 0.49 to 0.57

We are 95% sure that the true proportion of U.S. adults who are dissatisfied with the quality of education students receive in kindergarten through grade 12 is between 0.49 and 0.57 (i.e., 49% and 57%).0.49 to 0.57

We are 95% sure that the true proportion of U.S. adults who are dissatisfied with the quality of education students receive in kindergarten through grade 12 is between 0.49 and 0.57 (i.e., 49% and 57%).

B) 0.51 to 0.55

We are 95% sure that the true proportion of U.S. adults who are dissatisfied with the quality of education students receive in kindergarten through grade 12 is between 0.51 and 0.55 (i.e., 51% and 55%).

C) 0.51 to 0.55

We are 95% sure that the proportion of U.S. adults who reported being dissatisfied with the quality of education students receive in kindergarten through grade 12 is between 0.51 and 0.55 (i.e., 51% and 55%).

D) 0.49 to 0.57

We are 95% sure that the proportion of U.S. adults who reported being dissatisfied with the quality of education students receive in kindergarten through grade 12 is between 0.49 and 0.57 (i.e., 49% and 57%).

Diff: 2 Type: BI Var: 1

L.O.: 3.2.1;3.2.4

Use the following to answer the questions below:

Identify if each of the following statements is a proper interpretation of a 95% confidence interval.

10) I am 95% sure that this interval will contain the population parameter.

A) Correct

B) Incorrect

Diff: 2 Type: BI Var: 1

L.O.: 3.2.4

11) I am 95% sure that this interval will contain the sample statistic.

A) Correct

B) Incorrect

Diff: 2 Type: BI Var: 1

L.O.: 3.2.4

12) 95% of the population values will fall within this interval.

A) Correct

B) Incorrect

Diff: 2 Type: BI Var: 1

L.O.: 3.2.4

13) The probability that the population parameter is in this interval is 0.95.

A) Correct

B) Incorrect

Diff: 2 Type: BI Var: 1

L.O.: 3.2.4

14) 95% of the possible samples from this population will have sample statistics in this particular interval.

A) Correct

B) Incorrect

Diff: 3 Type: BI Var: 1

L.O.: 3.2.4

15) Recently, the Centers for Disease Control and Prevention estimated 9.4% of children under the age of 18 had asthma. They reported the standard error to be 0.35%. Assuming that the sampling distribution is symmetric and bell-shaped, find a 95% confidence interval.

A) 8.7% to 10.1%

B) 9.1% to 7.8%

C) 8.4% to 10.5%

D) 8.1% to 10.8%

Diff: 2 Type: BI Var: 1

L.O.: 3.2.3

Use the following to answer the questions below:

A sample of 148 college students reports sleeping an average of 6.85 hours on weeknights, with a margin of error of 0.35 hours. Based on this information, identify each of the following as plausible or not for the average amount of sleep college students get on weeknights.

16) 6.6 hours

A) Plausible

B) Not plausible

Diff: 2 Type: BI Var: 1

L.O.: 3.2.2

17) 7.5 hours

A) Plausible

B) Not plausible

Diff: 2 Type: BI Var: 1

L.O.: 3.2.2

18) 8 hours

A) Plausible

B) Not plausible

Diff: 2 Type: BI Var: 1

L.O.: 3.2.2

Use the following to answer the questions below:

In a poll conducted before a Massachusetts city's mayoral election, 134 of 420 randomly chosen likely voters indicated that they planned to vote for the Democratic candidate.

19) Compute a sample statistic from these data. Report your answer with three decimal places.

Diff: 2 Type: SA Var: 1

L.O.: 3.1.2

20) Suppose that an article describing the poll says that the margin of error for the statistic is 0.045. Use this information to find an interval estimate. Report your answer with three decimal places.

Diff: 2 Type: SA Var: 1

L.O.: 3.2.1

21) Suppose that an article describing the poll says that the margin of error for the statistic is 0.045 and an interval estimate is found.What quantity is the interval estimate in trying to capture? Identify with appropriate notation and words.

A) p = proportion of likely voters who plan to vote for the Democratic candidate

B) = proportion of likely voters who plan to vote for the Democratic candidate

C) μ = the mean number of voters who plan to vote for the Democratic candidate

D) = the mean number of voters who plan to vote for the Democratic candidate

Diff: 2 Type: BI Var: 1

L.O.: 3.1.1;3.2.0

22) Suppose that an article describing the poll says that the margin of error for the statistic is 0.045. Use this information to find an interval estimate and interpret the confidence interval.

Diff: 2 Type: ES Var: 1

L.O.: 3.2.4

23) Suppose that a student collects pulse rates from a random sample of 200 students at her college and finds a 90% confidence interval goes from 65.5 to 71.8 beats per minute. Is the following statement an appropriate interpretation of this interval? If not, explain why not.

"90% of the students at my college have mean pulse rates between 65.5 and 71.8 beats per minute."

Diff: 3 Type: ES Var: 1

L.O.: 3.2.4

3.3 Constructing Bootstrap Confidence Intervals

Use the following to answer the questions below:

Identify whether each of the following samples is a possible bootstrap sample from this original sample: 20, 24, 19, 23, 18

1) 24, 18, 23

A) Possible

B) Not Possible

Diff: 2 Type: BI Var: 1

L.O.: 3.3.1

2) 24, 19, 24, 20,23

A) Possible

B) Not Possible

Diff: 2 Type: BI Var: 1

L.O.: 3.3.1

3) 20, 24, 21, 19, 18

A) Possible

B) Not Possible

Diff: 2 Type: BI Var: 1

L.O.: 3.3.1

4) 20, 20, 20, 20, 20

A) Possible

B) Not Possible

Diff: 2 Type: BI Var: 1

L.O.: 3.3.1

5) 18, 19, 20, 23, 24

A) Possible

B) Not Possible

Diff: 2 Type: BI Var: 1

L.O.: 3.3.1

6) A sample of size 46 with a mean of 13.6 is to be used to construct a confidence interval for μ. A bootstrap distribution based on 1,000 samples is created. Where will the bootstrap distribution be centered?

A) 46

B) 13.6

C) μ

D) 1,000

Diff: 2 Type: BI Var: 1

L.O.: 3.3.2

7) A sample of n = 10 Illinois gas stations had an average price of $3.975 per gallon. The national average at this time was $3.63. If we want to use the sample data to construct a 95% confidence interval for the average gas price in Illinois, where would the bootstrap distribution be centered?

A) 3.63

B) 3.80

C) 3.975

D) 10

Diff: 2 Type: BI Var: 1

L.O.: 3.3.2

8) A bootstrap distribution will be centered at the value of the original statistic.

Diff: 2 Type: TF Var: 1

L.O.: 3.3.2

3.4 Bootstrap Confidence Intervals Using Percentiles

1) Decreasing the confidence level (say, from 95% to 85%) will cause the width of a typical confidence interval to ________.

A) increase

B) decrease

C) remain the same

Diff: 2 Type: BI Var: 1

L.O.: 3.4.3

Use the following to answer the questions below:

An Internet provider contacts a random sample of 300 customers and asks how many hours per week the customers use the Internet. It found the average amount of time spent on the Internet per week to be about 7.2 hours.

2) Define the parameter of interest, using the proper notation.

A) μ = mean number of hours per week all customers use the Internet

B) = 7.2 hours

C) = mean number of hours per week all customers use the Internet

D) μ = 7.2 hours

Diff: 2 Type: BI Var: 1

L.O.: 3.1.1

3) Use the information from the sample to give the best estimate of the population parameter.

A) = 7.2 hours

B) μ = mean number of hours per week all customers use the Internet

C) = mean number of hours per week all customers use the Internet

D) μ = 7.2 hours

Diff: 1 Type: BI Var: 1

L.O.: 3.1.2

4) Describe how to use the data to select one bootstrap sample. What statistic is recorded from this sample?

Diff: 3 Type: ES Var: 1

L.O.: 3.3.1;3.4.2

5) The standard error is about 0.458. Find a 95% confidence interval for the parameter. Round the margin of error to two decimal places.

A) 6.28 to 8.12 hours

B) 7.04 to 7.66 hours

C) 5.82 to 8.58 hours

D) 6.77 to 7.43 hours

Diff: 2 Type: BI Var: 1

L.O.: 3.2.3;3.2.4

6) Percentiles of the bootstrap distribution are provided. Use the percentiles to report a 95% confidence interval for the parameter.

A) 6.322 hours to 8.082 hours

B) 6.438 hours to 7.947 hours

C) 6.174 hours to 8.304 hours

D) 6.593 hours to 7.78 hours

Diff: 2 Type: BI Var: 1

L.O.: 3.4.1

7) Percentiles of the bootstrap distribution are provided. Use the percentiles to report a 90% confidence interval for the parameter.

A) 6.438 hours to 7.947 hours

B) 6.322 hours to 8.082 hours

C) 6.174 hours to 8.304 hours

D) 6.593 hours to 7.78 hours

Diff: 2 Type: BI Var: 1

L.O.: 3.4.1

Use the following to answer the questions below:

Suppose that a 95% confidence interval for the slope of a regression line based on a sample of size n = 100 and the percentiles of the slopes for 1,000 bootstrap samples goes from 2.50 to 2.80. For each change described (with all else staying the same), indicate which of the three confidence intervals would be the most likely result.

8) Decrease the sample size to n = 60.

A) 2.53 to 2.77 (narrower)

B) 2.50 to 2.80 (the same)

C) 2.46 to 2.84 (wider)

Diff: 3 Type: BI Var: 1

L.O.: 3.4.3

9) Increase the confidence level to 99%.

A) 2.53 to 2.77 (narrower)

B) 2.50 to 2.80 (the same)

C) 2.46 to 2.84 (wider)

Diff: 3 Type: BI Var: 1

L.O.: 3.4.3

10) Increase the number of bootstrap samples to 5,000.

A) 2.53 to 2.77 (narrower)

B) 2.50 to 2.80 (the same)

C) 2.46 to 2.84 (wider)

Diff: 3 Type: BI Var: 1

L.O.: 3.3.0;3.4.2

Use the following to answer the questions below:

Suppose we are interested in comparing the proportion of male students who smoke to the proportion of female students who smoke. We have a random sample of 150 students (60 males and 90 females) that includes two variables: Smoke = "yes" or "no" and Gender = "female (F)" or "male (M)." The two-way table below summarizes the results.

11) If the parameter of interest is the difference in proportions, pm - pf, where pm and pf represent the proportion of smokers in each gender, find a point estimate for this difference in proportions based on the data in the table. Report your answer with two decimal places.

Diff: 2 Type: SA Var: 1

L.O.: 3.1.2

12) Describe how to use the data to construct a bootstrap distribution. What value should be recorded for each of the bootstrap samples.

Diff: 2 Type: ES Var: 1

L.O.: 3.3.1;3.4.2

13) Use technology to construct a bootstrap distribution with at least 1,000 samples and estimate the standard error.

A) SE = 0.056

B) SE = 0.067

C) SE = 0.072

D) SE = 0.079

Diff: 2 Type: BI Var: 1

L.O.: 3.3.3;3.3.4

14) Use the estimate of the standard error to construct a 95% confidence interval for the difference in the proportion of smokers between male and female students, Round the margin of error to three decimal places. Provide an interpretation of the interval in the context of this data situation.

We are 95% sure that the difference in the proportion of smokers between male and female students is between -0.062 and 0.162.

Diff: 2 Type: ES Var: 1

L.O.: 3.2.3;3.3.5

15) You wish to provide a 98% confidence interval for the difference in the proportion of smokers between male and female students. State which percentiles of your bootstrap distribution you would use.

A) Use the 1%- and 99%-tiles

B) Use the 2%- and 98%-tiles

C) Use the 4%- and 96%-tiles

D) Use the 5%- and 95%-tiles

Diff: 2 Type: BI Var: 1

L.O.: 3.4.1

Use the following to answer the questions below:

Suppose we are interested in comparing the proportion of male students who smoke to the proportion of female students who smoke. We have a random sample of 150 students (60 males and 90 females) that includes two variables: Smoke = "yes" or "no" and Gender = "female (F)" or "male (M)." The two-way table below summarizes the results.

16) If the parameter of interest is the difference in proportions, - , where and , represent the proportion of smokers in each gender, find a point estimate for this difference in proportions based on the data in the table. Report your answer with two decimal places.

Diff: 2 Type: SA Var: 1

L.O.: 3.1.2

17) Describe how to use the data to construct a bootstrap distribution. What value should be recorded for each of the bootstrap samples.

Diff: 2 Type: ES Var: 1

L.O.: 3.3.1;3.4.2

18) Where should the bootstrap distribution be centered?

A) 0.0

B) 0.05

C) 0.10

D) 0.15

Diff: 2 Type: BI Var: 1

L.O.: 3.3.2

19) Describe how you would estimate the standard error from the bootstrap distribution.

Diff: 2 Type: ES Var: 1

L.O.: 3.3.4

20) The standard error is estimated to be 0.056. Find (in the context of this data situation) a 95% confidence interval for the difference in the proportion of smokers between male and female students, Round the margin of error to three decimal places.

A) -0.062 to 0.162

B) -0.006 to 0.106

C) -0.118 to 0.218

D) 0.475 to 0.525

Diff: 2 Type: BI Var: 1

L.O.: 3.2.3

21) Percentiles of the bootstrap distribution (based on 5,000 samples) are provided. Use the percentiles to provide a 98% confidence interval for the difference in the proportion of smokers between male and female students.

A) -0.078 to 0.189

B) -0.056 to 0.164

C) -0.039 to 0.144

D) -0.022 to 0.122

Diff: 2 Type: BI Var: 1

L.O.: 3.4.1

Use the following to answer the questions below:

To create a confidence interval from a bootstrap distribution using percentiles, we keep the middle values and chop off a certain percentage from each tail. Indicate what percent of values must be chopped off from each tail for each confidence level.

22) 95%

Diff: 2 Type: SA Var: 1

L.O.: 3.4.1

23) 88%

Diff: 2 Type: SA Var: 1

L.O.: 3.4.1

24) 99%

Diff: 2 Type: SA Var: 1

L.O.: 3.4.1

25) 80%

Diff: 2 Type: SA Var: 1

L.O.: 3.4.1

26) 96%

Diff: 2 Type: SA Var: 1

L.O.: 3.4.1

Use the following to answer the questions below:

There are 24 students enrolled in an introductory statistics class at a small university. As an in-class exercise the students were asked how many hours of television they watch each week. Their responses, broken down by gender, are summarized in the provided table. Assume that the students enrolled in the statistics class are representative of all students at the university.

Male	3	1	12	12	0	4	10	4	5	5	2	10	10	= 6
Female	10	3	2	10	3	2	0	1	6	1	5			= 3.91

27) If the parameter of interest is the difference in means, - where and are the mean number of hours spent watching television for males and females at this university, find a point estimate of the parameter based on the available data. Report your answer with two decimal places.

Diff: 2 Type: SA Var: 1

L.O.: 3.1.2

28) Describe how to use the data to construct a bootstrap distribution. What value should be recorded for each of the bootstrap samples?

Diff: 2 Type: ES Var: 1

L.O.: 3.3.1;3.4.2

29) If the parameter of interest is the difference in means, - where and are the mean number of hours spent watching television for males and females at this university, use technology to construct a bootstrap distribution with at least 1,000 samples and estimate the standard error.

A) SE = 1.511

B) SE = 2.283

C) SE = 3.022

D) SE = 18.132

Diff: 2 Type: BI Var: 1

L.O.: 3.3.3

30) Estimate the standard error and construct a 95% confidence interval for the difference in the mean number of hours spent watching television for males and females at this university. Round the margin of error to two decimal places.

A) -0.93 to 5.11

B) -2.48 to 6.66

C) 0.89 to 6.93

D) -0.66 to 8.48

Diff: 2 Type: BI Var: 1

L.O.: 3.2.3;3.3.5

31) Suppose another class does the same in class exercise and gets a 95% confidence interval of -0.86 to 5.34 for the difference in the mean number of hours spent watching television for males and females at this university. Interpret this 95% confidence interval in the context of this data situation.

Diff: 2 Type: ES Var: 1

L.O.: 3.2.4

32) You wish to provide a 95% confidence interval for the difference in the mean number of hours spent watching television for males and females at this university based on a bootstrap distribution. Which percentiles would you use?

A) The 2.5%- and 97.5%-iles

B) The 5%- and 95%-iles

C) The 10%- and 95%-iles

D) The 10%- and 90%-iles

Diff: 2 Type: BI Var: 1

L.O.: 3.4.1

Use the following to answer the questions below:

There are 24 students enrolled in an introductory statistics class at a small university. As an in-class exercise the students were asked how many hours of television they watch each week. Their responses, broken down by gender, are summarized in the provided table. Assume that the students enrolled in the statistics class are representative of all students at the university.

Male	3	1	12	12	0	4	10	4	5	5	2	10	10	= 6
Female	10	3	2	10	3	2	0	1	6	1	5			= 3.91

33) If the parameter of interest is the difference in means, - where and are the mean number of hours spent watching television for males and females at this university, find a point estimate of the parameter based on the available data. Report your answer with two decimal places.

Diff: 2 Type: SA Var: 1

L.O.: 3.1.2

34) Describe how to use the data to construct a bootstrap distribution. What value should be recorded for each of the bootstrap samples?

Diff: 2 Type: ES Var: 1

L.O.: 3.3.1;3.4.2

35) Where should the bootstrap distribution be centered?

A) 0

B) 2.09

C) 3.91

D) 6

Diff: 2 Type: BI Var: 1

L.O.: 3.3.2

36) Describe how you would estimate the standard error from the bootstrap distribution.

Diff: 2 Type: ES Var: 1

L.O.: 3.3.4

37) The standard error is estimated to be 1.511 (based on 5,000 bootstrap samples). Find a 95% confidence interval for the difference in the mean number of hours spent watching television for males and females at this university. Round the margin of error to two decimal places.

Diff: 2 Type: SA Var: 1

L.O.: 3.2.3;3.3.5

38) The standard error is estimated to be 1.511. Construct and interpret the 95% confidence interval in the context of this data situation.

Diff: 2 Type: ES Var: 1

L.O.: 3.2.4

39) Percentiles of the bootstrap distribution (based on 5,000 samples) are provided. Use the percentiles to provide a 95% confidence interval for the difference in the mean number of hours spent watching television for males and females at this university. Indicate which percentiles you are using.

A) -0.888 to 4.972

B) -1.497 to 5.657

C) -0.395 to 4.573

D) -0.189 to 4.056

Diff: 2 Type: BI Var: 1

L.O.: 3.4.1

Use the following to answer the questions below:

November 6, 2012 was election day. Many of the major television networks aired coverage of the incoming election results during the primetime hours. The provided table displays the amount of time (in minutes) spent watching election coverage for a random sample of 25 U.S. adults.

40) What is the population parameter of interest? Define using the appropriate notation.

Diff: 2 Type: ES Var: 1

L.O.: 3.1.1

41) Use the data from the sample to estimate the parameter of interest. Report your answer with two decimal places.

A) = 80.44 minutes

B) = 70.00 minutes

C) μ = 80.44 minutes

D) μ = 70.00 minutes

Diff: 2 Type: BI Var: 1

L.O.: 3.1.2

42) Describe how to use the data to construct a bootstrap distribution. What value should be recorded for each of the bootstrap samples?

Diff: 2 Type: ES Var: 1

L.O.: 3.3.1;3.4.2

43) Use technology to construct a bootstrap distribution with at least 1,000 samples and estimate the standard error.

A) SE = 8.769

B) SE = 17.538

C) SE = 11.471

D) SE = 22.942

Diff: 2 Type: BI Var: 1

L.O.: 3.3.3;3.3.4

44) Use the estimate of the standard error to construct a 95% confidence interval for the mean amount of time (in minutes) U.S. adults spent watching election coverage on election night. Use three decimal places in your answer.

A) 62.902 to 97.978 minutes

B) 71.671 to 89.209 minutes

C) 52.462 to 87.538 minutes

D) 58.529 to 81.471 minutes

Diff: 2 Type: BI Var: 1

L.O.: 3.2.3;3.3.4

45) Suppose you wish to use the percentiles of your bootstrap distribution to provide a 92% confidence interval for the mean amount of time (in minutes) U.S. adults spent watching election coverage on election night. Which percentiles would you use?

A) The 4%- and 96%-iles.

B) The 1%- and 99%-iles.

C) The 2%- and 98%-iles.

D) The 5%- and 95%-iles.

Diff: 2 Type: BI Var: 1

L.O.: 3.4.1

46) Interpret your 92% confidence interval in the context of this data situation.

Diff: 2 Type: ES Var: 1

L.O.: 3.2.4

Use the following to answer the questions below:

November 6, 2012 was election day. Many of the major television networks aired coverage of the incoming election results during the primetime hours. The provided table displays the amount of time (in minutes) spent watching election coverage for a random sample of 25 U.S. adults.

47) What is the population parameter of interest? Define using the appropriate notation.

Diff: 2 Type: ES Var: 1

L.O.: 3.1.1

48) Use the data from the sample to estimate the parameter of interest. Report your answer with two decimal places.

A) = 80.44 minutes

B) μ = 70.00 minutes

C) μ = 80.44 minutes

D) = 70.00 minutes

Diff: 2 Type: BI Var: 1

L.O.: 3.1.2

49) Describe how to use the data to construct a bootstrap distribution. What value should be recorded for each of the bootstrap samples?

Diff: 2 Type: ES Var: 1

L.O.: 3.3.1;3.4.2

50) Where should the bootstrap distribution be centered?

A) 25

B) 60

C) 80.44

D) 100

Diff: 2 Type: BI Var: 1

L.O.: 3.3.2

51) Describe how you would estimate the standard error from the bootstrap distribution.

Diff: 2 Type: ES Var: 1

L.O.: 3.3.4

52) The standard error is estimated to be 8.769 (based on 5,000 bootstrap samples). Find a 95% confidence interval for the mean amount of time (in minutes) U.S. adults spent watching election coverage on election night. Round the margin of error to two decimal places.

A) 62.90 to 97.98 minutes

B) 52.462 to 87.538 minutes

C) 71.671 to 89.209 minutes

D) 58.529 to 81.471 minutes

Diff: 2 Type: BI Var: 1

L.O.: 3.2.3;3.3.5

53) Percentiles of the bootstrap distribution (based on 5,000 samples) are provided. Use the percentiles to provide a 92% confidence interval for the mean amount of time (in minutes) U.S. adults spent watching election coverage on election night. Indicate which percentiles you are using.

A) 65.160 to 95.780 minutes (use the 4%- and 96%-iles)

B) 63.000 to 98.540 minutes (use the 2%- and 98%-iles)

C) 66.880 to 94.080 minutes (use the 6%- and 94%-iles)

D) 68.240 to 92.740 minutes (use the 8%- and 92%-iles)

Diff: 2 Type: BI Var: 1

L.O.: 3.4.1

54) Interpret your 92% confidence interval in the context of this data situation.

Diff: 2 Type: ES Var: 1

L.O.: 3.2.4

Use the following to answer the following questions:

A study to investigate the dominant paws in cats was described in the scientific journal Animal Behaviour. The researchers used a random sample of 42 domestic cats. In this study, each cat was shown a treat (5 grams of tuna), and while the cat watched, the food was placed inside a jar. The opening of the jar was small enough that the cat could not stick its head inside to remove the treat. The researcher recorded the paw that was first used by the cat to try to retrieve the treat. This was repeated 100 times for each cat (over a span of several days). The paw used most often was deemed the dominant paw (note that one cat used both paws equally and was classified as "ambidextrous"). Of the 42 cats studied, 20 were classified as "left-pawed."

55) What is the population parameter of interest? Define using the appropriate notation.

Diff: 2 Type: ES Var: 1

L.O.: 3.1.1

56) Use the data from the sample to estimate the parameter of interest. Report your answer with three decimal places.

Diff: 1 Type: SA Var: 1

L.O.: 3.1.2

57) Describe how to use the data to construct a bootstrap distribution. What value should be recorded for each of the bootstrap samples?

Diff: 2 Type: ES Var: 1

L.O.: 3.3.1;3.4.2

58) Use technology to construct a bootstrap distribution with at least 1,000 samples and estimate the standard error.

A) SE = 0.078

B) SE = 0.042

C) SE = 0.156

D) SE = 0.636

Diff: 2 Type: BI Var: 1

L.O.: 3.3.3;3.3.4

59) Suppose you estimate of the standard error to be 0.056. Construct a 95% confidence interval for the proportion of domestic cats that are "left-pawed". Round the margin of error to three decimal places.

A) 0.364 to 0.588

B) 0.420 to 0.532

C) 0.392 to 0.560

D) 0.402 to 0.550

Diff: 2 Type: BI Var: 1

L.O.: 3.2.3;3.3.5

60) Use technology to construct a bootstrap distribution with at least 1,000 samples. Use the percentiles of your bootstrap distribution to provide a 99% confidence interval for the parameter. Indicate the percentiles that you use.

A) 0.262 to 0.667 (using the 0.5%- and 99.5%-iles)

B) 0.286 to 0.643 (use 1%- and 99%-iles)

C) 0.310 to 0.619 (use 2.5%- and 97.5%-iles)

D) 0.357 to 0.595 (use 5%- and 95%-iles)

Diff: 2 Type: BI Var: 1

L.O.: 3.4.1

61) Construct a 99% confidence interval and provide an interpretation of it in the context of this data situation.

Diff: 2 Type: ES Var: 1

L.O.: 3.2.4

62) The researchers were also interested in comparing the proportion of "left-pawed" cats for male and female cats. Of the 21 male cats in the sample, 19 were classified as "left-pawed" while only 1 of the 21 female cats was considered to be "left-pawed."

A bootstrap distribution (based on 1,000 bootstrap samples) for difference in the proportion of "left-pawed" cats is provided. Would it be appropriate to use this bootstrap distribution to construct a confidence interval for the difference in the proportion of male and female cats that are "left-pawed"?

A) Yes

B) No

Diff: 3 Type: MC Var: 1

L.O.: 3.4.4

Use the following to answer the questions below:

A study to investigate the dominant paws in cats was described in the scientific journal Animal Behaviour. The researchers used a random sample of 42 domestic cats. In this study, each cat was shown a treat (5 grams of tuna), and while the cat watched, the food was placed inside a jar. The opening of the jar was small enough that the cat could not stick its head inside to remove the treat. The researcher recorded the paw that was first used by the cat to try to retrieve the treat. This was repeated 100 times for each cat (over a span of several days). The paw used most often was deemed the dominant paw (note that one cat used both paws equally and was classified as "ambidextrous"). Of the 42 cats studied, 20 were classified as "left-pawed."

63) What is the population parameter of interest? Define using the appropriate notation.

Diff: 2 Type: ES Var: 1

L.O.: 3.1.1

64) Use the data from the sample to estimate the parameter of interest. Round your answer to three decimal places.

Diff: 1 Type: SA Var: 1

L.O.: 3.1.2

65) Describe how to use the data to construct a bootstrap distribution. What value should be recorded for each of the bootstrap samples?

Diff: 2 Type: ES Var: 1

L.O.: 3.3.1;3.4.2

66) Where should the bootstrap distribution be centered?

A) 0.476

B) 20

C) 42

D) 0.95

Diff: 2 Type: BI Var: 1

L.O.: 3.3.2

67) Describe how you would estimate the standard error from the bootstrap distribution.

Diff: 2 Type: ES Var: 1

L.O.: 3.3.4

68) The standard error is estimated to be 0.078 (based on 5,000 bootstrap samples). Find a 95% confidence interval for the proportion of domestic cats that are "left-pawed". Round the margin of error to three decimal places.

A) 0.320 to 0.632

B) .398 to 0.554

C) 0.262 to 0.667

D) 0.286 to 0.643

Diff: 2 Type: BI Var: 1

L.O.: 3.2.3;3.3.5

69) Percentiles of the bootstrap distribution (based on 5,000 samples) are provided. Use the percentiles to provide a 99% confidence interval for the parameter. Indicate the percentiles that you use.

A) 0.262 to 0.667 (use 0.5%- and 99.5%-iles)

B) 0.286 to 0.643 (use 1%- and 99%-iles)

C) 0.310 to 0.619 (use 2.5%- and 97.5%-iles)

D) 0.357 to 0.595 (use 5%- and 95%-iles)

Diff: 2 Type: BI Var: 1

L.O.: 3.4.1

70) Percentiles of the bootstrap distribution (based on 5,000 samples) are provided. Use the percentiles to provide a 99% confidence interval for the parameter. Provide an interpretation of your 99% confidence interval in the context of this data situation.

Diff: 2 Type: ES Var: 1

L.O.: 3.2.4

71) The researchers were also interested in comparing the proportion of "left-pawed" cats for male and female cats. Of the 21 male cats in the sample, 19 were classified as "left-pawed" while only 1 of the 21 female cats was considered to be "left-pawed".

A bootstrap distribution (based on 1,000 bootstrap samples) for difference in the proportion of "left-pawed" cats is provided. Would it be appropriate to use this bootstrap distribution to construct a confidence interval for the difference in the proportion of male and female cats that are "left-pawed"? Briefly explain.

Diff: 3 Type: ES Var: 1

L.O.: 3.4.4

72) A bootstrap distribution, based on 1,000 bootstrap samples is provided. Use the distribution to estimate a 99% confidence interval for the population mean. Explain how you arrived at your answer.

Diff: 3 Type: ES Var: 1

L.O.: 3.4.1

Use the following to answer the questions below:

A biologist collected data on a random sample of porcupines. She wants to estimate the correlation between the body mass of a porcupine (in grams) and the length of the porcupine (in cm).

73) Her sample consists of 20 porcupines. A bootstrap distribution for the correlation between body mass and length (based on 1,000 samples) is provided. Would it be appropriate to use this bootstrap distribution to estimate a 95% confidence interval for the correlation between body mass and length of porcupines?

A) Yes

B) No

Diff: 2 Type: MC Var: 1

L.O.: 3.4.4

74) The biologist noted that two of the porcupines were much smaller than the others, and thus they were likely not "adults". Since she is only interested in adult porcupines, the biologist wants to use the 18 adults to estimate the correlation between body mass and body length. The sample correlation is 0.407. Her bootstrap distribution is provided. The standard error is estimated to be 0.165.

If appropriate, construct and interpret a 95% confidence interval for the correlation between body mass and body length for adult porcupines (with the margin of error rounded to three decimal places). If not appropriate, explain why not.

0.407 ± 2*0.165 ⇒ 0.407 ± 0.33 ⇒ 0.077 to 0.737

We are 95% sure that the correlation between body mass and body length for adult porcupines is between 0.077 and 0.737.

Diff: 2 Type: ES Var: 1

L.O.: 3.2.3;3.2.4;3.3.5;3.4.4

Use the following to answer the questions below:

In a survey conducted by the Gallup organization, 1,017 adults were asked, "In general, how much trust and confidence do you have in the mass media — such as newspapers, TV, and radio — when it comes to reporting the news fully, accurately, and fairly?" 81 said that they had a "great deal" of confidence, 325 said they had a "fair amount" of confidence, 397 said they had "not very much" confidence, and 214 said they had "no confidence at all."

75) Suppose the parameter of interest is the proportion of U.S. adults who have "no confidence at all" in the media. Use the data to find an estimate of this parameter. Report your answer with two decimal places.

Diff: 2 Type: SA Var: 1

L.O.: 3.1.2

76) Describe how to use the data to construct a bootstrap distribution. What value should be recorded for each of the bootstrap samples?

Diff: 2 Type: ES Var: 1

L.O.: 3.3.1;3.4.2

77) Use technology to construct a bootstrap distribution with at least 1,000 samples and estimate the standard error.

A) SE = 0.013

B) SE = 0.026

C) SE = 0.001

D) SE = 0.002

Diff: 2 Type: BI Var: 1

L.O.: 3.3.3;3.3.4

78) Use the estimate of the standard error to construct a 95% confidence interval for the proportion of U.S. adults who have no confidence in the media. Round the margin of error to three decimal places.

A) 0.184 to 0.236

B) 0.197 to 0.223

C) 0.394 to 0.446

D) 0.407 to 0.433

Diff: 2 Type: BI Var: 1

L.O.: 3.2.3;3.3.5

79) Construct a 95% confidence interval for the proportion of U.S. adults who have no confidence in the media. Provide an interpretation of your 95% confidence interval in the context of this data situation.

Diff: 2 Type: ES Var: 1

L.O.: 3.2.4

80) Suppose you wish to use the percentiles of your bootstrap distribution to provide a 95% confidence interval for the proportion of U.S. adults who have no confidence in the media. Which percentiles would you use?

A) The 2.5%- and 97.5%-tiles.

B) The 1%- and 99%-tiles.

C) The 5%- and 95%-tiles.

D) The 10%- and 90%-tiles.

Diff: 2 Type: BI Var: 1

L.O.: 3.4.1

Use the following to answer the questions below:

In a survey conducted by the Gallup organization, 1,017 adults were asked "In general, how much trust and confidence do you have in the mass media — such as newspapers, TV, and radio — when it comes to reporting the news fully, accurately, and fairly?" 81 said that they had a "great deal" of confidence, 325 said they had a "fair amount" of confidence, 397 said they had "not very much" confidence, and 214 said they had "no confidence at all."

81) Suppose the parameter of interest is the proportion of U.S. adults who have "no confidence at all" in the media. Use the data to find an estimate of this parameter. Report your answer with two decimal places.

Diff: 2 Type: SA Var: 1

L.O.: 3.1.2

82) Describe how to use the data to construct a bootstrap distribution. What value should be recorded for each of the bootstrap samples?

Diff: 2 Type: ES Var: 1

L.O.: 3.3.1;3.4.2

83) Describe how you would estimate the standard error from the bootstrap distribution.

Diff: 2 Type: ES Var: 1

L.O.: 3.3.4

84) The estimate of the standard error is 0.013. Use the estimate of the standard error to construct a 95% confidence interval for the proportion of U.S. adults who have no confidence in the media. Round the margin of error to three decimal places.

A) 0.184 to 0.236

B) 0.197 to 0.223

C) 0.190 to 0.231

D) 0.194 to 0.227

Diff: 2 Type: BI Var: 1

L.O.: 3.2.3;3.3.5

85) Construct a 95% confidence interval for the proportion of U.S. adults who have no confidence in the media. Provide an interpretation of your 95% confidence interval in the context of this data situation.

Diff: 2 Type: ES Var: 1

L.O.: 3.2.4

86) Percentiles of the bootstrap distribution (based on 5,000 samples) are provided. Which percentiles would you use 95% confidence interval for the proportion of U.S. adults who have no confidence in the media?

A) The 2.5%- and 97.5%-tiles.

B) The 1%- and 99%-tiles.

C) The 5%- and 95%-tiles.

D) The 10%- and 90%-tiles.

Diff: 2 Type: BI Var: 1

L.O.: 3.4.1

87) In a dotplot of a bootstrap distribution, the number of dots should match the size of the original sample.

Diff: 2 Type: TF Var: 1

L.O.: 3.3.0;3.4.2

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