1. Active Learning Lecture Slides For use with Classroom Response Systems
Statistical Inference: Confidence Intervals

2. 8.1 A good point estimate has which of the following characteristics?
a) Bias: None Standard Error: High
b) Bias: High Standard Error: High
c) Bias: None Standard Error: Low
d) Bias: High Standard Error: Low
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3. 8.1 A good point estimate has which of the following characteristics?
a) Bias: None Standard Error: High
b) Bias: High Standard Error: High
c) Bias: None Standard Error: Low
d) Bias: High Standard Error: Low
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4. d) Point estimate 1.96*standard error
8.2 When the sampling distribution is approximately normal, what is the margin of error equal to for a 95% confidence interval?
a) 1.96
b) 1.96*standard error
c) Standard error
d) Point estimate *standard error
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5. d) Point estimate 1.96*standard error
8.2 When the sampling distribution is approximately normal, what is the margin of error equal to for a 95% confidence interval?
a) 1.96
b) 1.96*standard error
c) Standard error
d) Point estimate *standard error
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6. 8.3 In 2006 the GSS had a special topic that investigated disabilities. They asked respondents if they had difficulty fully participating in school, housework or other daily activities and 265 out of 2,749 said “yes”. What is the point estimate of the population proportion of Americans that have difficulty completing these tasks?
a) 0.10
b) 0.097
c) 0.265
d) p
e) Unknown
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7. 8.3 In 2006 the GSS had a special topic that investigated disabilities. They asked respondents if they had difficulty fully participating in school, housework or other daily activities and 265 out of 2,749 said “yes”. What is the point estimate of the population proportion of Americans that have difficulty completing these tasks?
a) 0.10
b) 0.097
c) 0.265
d) p
e) Unknown
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8. 8.4 True or False: A point estimate is better than an interval estimate because it gives you the exact value for which you are looking.
a) True
b) False
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9. 8.4 True or False: A point estimate is better than an interval estimate because it gives you the exact value for which you are looking.
a) True
b) False
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10. 8.5 True or False: An interval estimate gives you a region that the parameter has to fall within.
a) True
b) False
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11. 8.5 True or False: An interval estimate gives you a region that the parameter has to fall within.
a) True
b) False
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12. 8.6 The formula below gives a region of plausible values of :
a) the population proportion
b) the population mean
c) the sample mean
d) the sample proportion
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13. 8.6 The formula below gives a region of plausible values of :
a) the population proportion
b) the population mean
c) the sample mean
d) the sample proportion
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14. a) Yes, there are more than 30 observations.
8.7 In 2006 the GSS asked 2,986 people if they were very happy, pretty happy, or not too happy and 920 people said that they were very happy. Is the sample “large” enough to calculate the 95% confidence interval to estimate the proportion of all Americans that are very happy?
a) Yes, there are more than 30 observations.
b) Yes, there are more than 15 successes and 15
failures.
c) No, there are not more than 15 successes and 15
d) Cannot be determined.
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15. a) Yes, there are more than 30 observations.
8.7 In 2006 the GSS asked 2,986 people if they were very happy, pretty happy, or not too happy and 920 people said that they were very happy. Is the sample “large” enough to calculate the 95% confidence interval to estimate the proportion of all Americans that are very happy?
a) Yes, there are more than 30 observations.
b) Yes, there are more than 15 successes and 15
failures.
c) No, there are not more than 15 successes and 15
d) Cannot be determined.
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16. 8.8 In 2006 the GSS asked 2,986 people if they were very happy, pretty happy, or not too happy and 920 people said that they were very happy. Find the 95% confidence interval to estimate the proportion of all Americans that are very happy.
a) (0, 0.02)
b) (0.25, 0.37)
c) (0.27, 0.35)
d) (0.29, 0.32)
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17. 8.8 In 2006 the GSS asked 2,986 people if they were very happy, pretty happy, or not too happy and 920 people said that they were very happy. Find the 95% confidence interval to estimate the proportion of all Americans that are very happy.
a) (0, 0.02)
b) (0.25, 0.37)
c) (0.27, 0.35)
d) (0.29, 0.32)
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18. 8.9 What is the correct z-score for a 97% confidence interval for the population proportion?
b) 1.96
c) 2.05
d) 2.17
e) None of the above
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19. 8.9 What is the correct z-score for a 97% confidence interval for the population proportion?
b) 1.96
c) 2.05
d) 2.17
e) None of the above
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20. a) A 90% confidence interval b) A 95% confidence interval
8.10 Based off of the same sample, which of the confidence intervals for the population mean would be the widest?
a) A 90% confidence interval
b) A 95% confidence interval
c) A 99% confidence interval
d) Cannot be determined
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21. a) A 90% confidence interval b) A 95% confidence interval
8.10 Based off of the same sample, which of the confidence intervals for the population mean would be the widest?
a) A 90% confidence interval
b) A 95% confidence interval
c) A 99% confidence interval
d) Cannot be determined
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22. a) the sample size decreases. b) the sample size increases.
8.11 The margin of error of a confidence interval of the population mean decreases as…
a) the sample size decreases.
b) the sample size increases.
c) the sample mean increases.
d) the sample mean decreases.
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23. a) the sample size decreases. b) the sample size increases.
8.11 The margin of error of a confidence interval of the population mean decreases as…
a) the sample size decreases.
b) the sample size increases.
c) the sample mean increases.
d) the sample mean decreases.
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24. 8.12 The General Social Survey included a question about how many hours the respondent spent doing religious activities outside of their own home. For the 1,414 respondents the sample mean was 6.15 hours and the sample standard deviation was hours. Find the 95% confidence interval for the population mean amount of time spent doing religious activities outside of their own home.
a) (5.43, 6.87)
b) (-26.24, 38.55)
c) (5.29, 7.01)
d) (5.03, 7.27)
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25. 8.12 The General Social Survey included a question about how many hours the respondent spent doing religious activities outside of their own home. For the 1,414 respondents the sample mean was 6.15 hours and the sample standard deviation was hours. Find the 95% confidence interval for the population mean amount of time spent doing religious activities outside of their own home.
a) (5.43, 6.87)
b) (-26.24, 38.55)
c) (5.29, 7.01)
d) (5.03, 7.27)
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26. d) Nothing can be determined.
8.13 The General Social Survey included a question about how many hours the respondent spent doing religious activities outside of their own home. For the 1,414 respondents the sample mean was 6.15 hours and the sample standard deviation was hours. What can we say about the distribution of hours spent doing religious activities?
a) It is bell shaped.
b) It is right skewed.
c) It is left skewed.
d) Nothing can be determined.
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27. d) Nothing can be determined.
8.13 The General Social Survey included a question about how many hours the respondent spent doing religious activities outside of their own home. For the 1,414 respondents the sample mean was 6.15 hours and the sample standard deviation was hours. What can we say about the distribution of hours spent doing religious activities?
a) It is bell shaped.
b) It is right skewed.
c) It is left skewed.
d) Nothing can be determined.
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28. 8.14 Which of the following is NOT a property of the t distribution?
a) It is symmetric.
b) It is indexed by a degree of freedom equal to
n - 1.
c) It has more spread in the tails than the normal distribution.
d) The shape becomes closer and closer to the normal distribution as n decreases.
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29. 8.14 Which of the following is NOT a property of the t distribution?
a) It is symmetric.
b) It is indexed by a degree of freedom equal to
n - 1.
c) It has more spread in the tails than the normal distribution.
d) The shape becomes closer and closer to the normal distribution as n decreases.
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30. 8.15 A marketing researcher is interested in estimating the mean amount of money spent on lunch by college students. The average amount spent on lunch by a random sample of 10 students is $6.30 with a standard deviation of $2.21. Find the 95% confidence interval for the population mean amount spent on lunch every day. b) c)
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31. 8.15 A marketing researcher is interested in estimating the mean amount of money spent on lunch by college students. The average amount spent on lunch by a random sample of 10 students is $6.30 with a standard deviation of $2.21. Find the 95% confidence interval for the population mean amount spent on lunch every day. b) c)
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32. 8. 16 In 2002 a local survey (using a SRS) found that 13
8.16 In 2002 a local survey (using a SRS) found that 13.4% of people strongly agreed with the statement that “More parking meters should be installed downtown.” Using the 2002 data as a guideline, determine the sample size needed to estimate the proportion of people that would agree for the current year within 0.01 at 95% confidence.
a) 4458
b) 3140
c) 45
d) 23
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33. 8. 16 In 2002 a local survey (using a SRS) found that 13
8.16 In 2002 a local survey (using a SRS) found that 13.4% of people strongly agreed with the statement that “More parking meters should be installed downtown.” Using the 2002 data as a guideline, determine the sample size needed to estimate the proportion of people that would agree for the current year within 0.01 at 95% confidence.
a) 4458
b) 3140
c) 45
d) 23
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34. 8.17 Suppose that you were interested in determining the proportion of Americans that agreed with the statement that “Taxes should not be raised for any reason.” Assuming that you have no idea what proportion will agree with this statement, determine the sample size needed to estimate the proportion of people that agree for the current year within 0.01 at 95% confidence.
a) 16,513
b) 9,604
c) 4,458
d) 4,900
e) 49
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35. 8.17 Suppose that you were interested in determining the proportion of Americans that agreed with the statement that “Taxes should not be raised for any reason.” Assuming that you have no idea what proportion will agree with this statement, determine the sample size needed to estimate the proportion of people that agree for the current year within 0.01 at 95% confidence.
a) 16,513
b) 9,604
c) 4,458
d) 4,900
e) 49
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36. e) Cannot be determined
8.18 Suppose that you are interested in estimating the population mean entry salary of engineers. You think that entry salaries probably range from $30,000 to $100,000 and the distribution of salaries is bell shaped. You want to be accurate to within $3,000 of the population mean entry salary and be 95% confident. What size sample do you need?
a) 100
b) 87
c) 59
d) 8
e) Cannot be determined
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37. e) Cannot be determined
8.18 Suppose that you are interested in estimating the population mean entry salary of engineers. You think that entry salaries probably range from $30,000 to $100,000 and the distribution of salaries is bell shaped. You want to be accurate to within $3,000 of the population mean entry salary and be 95% confident. What size sample do you need?
a) 100
b) 87
c) 59
d) 8
e) Cannot be determined
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38. e) Cannot be determined
8.19 Suppose that you want to estimate the entry level salaries of high school teachers for the state of Nebraska. A previous study had $1700 listed as the sample standard deviation. You want to have a 90% confidence interval with a margin of error of $250. How large a sample do you need?
a) 178
b) 126
c) 91
d) 12
e) Cannot be determined
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39. e) Cannot be determined
8.19 Suppose that you want to estimate the entry level salaries of high school teachers for the state of Nebraska. A previous study had $1700 listed as the sample standard deviation. You want to have a 90% confidence interval with a margin of error of $250. How large a sample do you need?
a) 178
b) 126
c) 91
d) 12
e) Cannot be determined
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40. d) Cannot be determined
8.20 Suppose that you are a writer for a university newspaper and due to time constraints you conduct a survey of only 20 randomly selected students. You ask them, “Do you plan to watch the homecoming parade?” and 19 of them say they plan to watch. Create a 95% confidence interval for the proportion of students that plan on watching the parade.
a) (0.85, 1)
b) (.74, 1)
c) (.76, .99)
d) Cannot be determined
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41. d) Cannot be determined
8.20 Suppose that you are a writer for a university newspaper and due to time constraints you conduct a survey of only 20 randomly selected students. You ask them, “Do you plan to watch the homecoming parade?” and 19 of them say they plan to watch. Create a 95% confidence interval for the proportion of students that plan on watching the parade.
a) (0.85, 1)
b) (.74, 1)
c) (.76, .99)
d) Cannot be determined
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42. 8.21 The margin of error of a confidence interval estimates the error…
a) caused by bad sampling techniques.
b) caused by measurement error.
c) caused by not controlling lurking variables.
d) caused by using a sample rather than the whole
population.
e) all of the above.
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43. 8.21 The margin of error of a confidence interval estimates the error…
a) caused by bad sampling techniques.
b) caused by measurement error.
c) caused by not controlling lurking variables.
d) caused by using a sample rather than the whole
population.
e) all of the above.
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44. a) repeatedly sampling from the population.
8.22 The bootstrap method is a method that constructs a confidence interval by…
a) repeatedly sampling from the population.
b) repeatedly sampling from the sample.
c) repeatedly sampling from the sampling
distribution.
d) none of the above.
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45. a) repeatedly sampling from the population.
8.22 The bootstrap method is a method that constructs a confidence interval by…
a) repeatedly sampling from the population.
b) repeatedly sampling from the sample.
c) repeatedly sampling from the sampling
distribution.
d) none of the above.
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46. 8.23 Why is the bootstrap method used?
a) Because it is easier than traditional methods.
b) Because it can be used when the formula for
the confidence interval cannot easily be found
mathematically.
c) Because it uses additional sampling – this
makes the confidence interval much better than
traditional methods.
d) Because it allows us to use 10,000 samples
rather than just 1 sample that is used in
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47. 8.23 Why is the bootstrap method used?
a) Because it is easier than traditional methods.
b) Because it can be used when the formula for
the confidence interval cannot easily be found
mathematically.
c) Because it uses additional sampling – this
makes the confidence interval much better than
traditional methods.
d) Because it allows us to use 10,000 samples
rather than just 1 sample that is used in
Copyright © 2013 Pearson Education, Inc.

48. a) Find the average and standard deviation of the
8.24 To make a 90% confidence interval for the population median using the bootstrap method you first randomly select 20,000 separate samples of size 8 from the original data and then you compute the medians from each of the new samples. What is the next step?
a) Find the average and standard deviation of the
20,000 medians. Then, compute a traditional 95%
confidence interval ( ) with those values.
b) Find the 2.5th and 97.5th percentile of the medians,
this is your confidence interval.
c) Find the 5th and 95th percentiles of the medians, this
is your confidence interval.
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49. a) Find the average and standard deviation of the
8.24 To make a 90% confidence interval for the population median using the bootstrap method you first randomly select 20,000 separate samples of size 8 from the original data and then you compute the medians from each of the new samples. What is the next step?
a) Find the average and standard deviation of the
20,000 medians. Then, compute a traditional 95%
confidence interval ( ) with those values.
b) Find the 2.5th and 97.5th percentile of the medians,
this is your confidence interval.
c) Find the 5th and 95th percentiles of the medians, this
is your confidence interval.
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