STAT 217 Unit 1-4 Study Review Questions with Correct Answers
(Grade A+)
Question 1: Random sampling is a more important consideration than random assignment if the
research question is whether students tend to receive higher scores on essays if they are encouraged to
submit a draft than if they are not so encouraged.
a) true
b) false
Answer: B. false
Question 2: Random sampling is a more important consideration than random assignment if the
research question is whether faculty tend to drive older cars than students drive on your campus.
a) true
b) false
Answer: A. true
Question 3: A randomized experiment allows for the possibility of drawing a cause-and-effect
conclusion between _________ and ________.
Answer: the explanatory and the response variable
Question 4: Which of the following must happen in a study to allow us to determine cause and effect?
Answer: Randomly assigning the observational units to different treatment groups
Question 5: One of the authors came across an article (USA Today, 2008) that said that on average
Americans have visited 16 states in the United States. Recall that in the author's sample of 50 students
the average number of states the students had visited was 9.48 and the standard deviation was 7.13. The
data are not strongly skewed. The 95% confidence interval for the average number of states all
students at the author's school have visited is (7.4537, 11.5063). Judge the validity of the following
statement: The 95% confidence interval that you calculated provides evidence that the average number
of states all students at the author's school have visited is different from 16.
a) True
b) False
Answer: A. true
Page 1
,Question 6: An instructor selected a random sample of students in her school and asked them how
many hours per week they expected to spend studying for their courses outside of class. The sample
average was 7.00 hours and the sample standard deviation was 4.19 hours. The data were not strongly
skewed. The theory-based 95% confidence interval for the parameter of interest was 5.6030 and 8.3970.
Judge the correctness of the following interpretation: We are 95% confident that the average
hours/week all students in this school will spend studying is between 5.6030 and 8.3970.
a) Not correct
b) Correct
Answer: B. Correct
Question 7: According to a 2011 report by the United States Department of Labor, civilian Americans
spend 2.75 hours per day watching television. A faculty researcher, Dr. Sameer, at California
Polytechnic State University (Cal Poly) conducts a study to see whether a different average applies to
Cal Poly students. Suppose that for a random sample of 100 Cal Poly students, the mean and standard
deviation of hours per day spent watching TV turns out to be 3.01 and 1.97 hours, respectively. The
data were used to find a 95% confidence interval: (2.619, 3.401) hours/day. Suppose that the data had
actually been collected from a sample of 150 students, and not 100, but everything else (mean and SD)
was the same as reported earlier. How, if at all, would the new 95% confidence interval based on these
data differ from the interval mentioned earlier: (2.619, 3.401) hours?
a) More information is needed to answer this question.
b) The new interval would be wider than (2.619, 3.401) hours, because the sample size is bigger.
c) The new interval would still be (2.619, 3.401) hours, because we are still 95% confident.
d) The new interval would be narrower than (2.619, 3.401) hours, because the sample size is bigger.
Answer: D. The new interval would be narrower than (2.619, 3.401) hours, because the sample size is
bigger.
Question 8: To estimate the proportion of city voters who will vote for the Republican candidate in the
election, two students, Manny and Nina, each decide to conduct polls in the city. Manny selects a
random sample of 50 voters, while Nina selects a random sample of 100 voters. Suppose both samples
result in 48% of the voters saying they will vote for the Republican candidate. Whose 95% confidence
interval will have the larger margin of error: Manny's or Nina's? How are you deciding?
a) Manny's; a small sample size will result in more variability and hence a wider interval.
b) Nina's; a large sample size will result in more variability and hence a wider interval. c)Neither; the sample
size does not affect the margin of error.
Answer: A. Manny's; a small sample size will result in more variability and hence a wider interval.
Page 2
,Question 9: A 2SD 95% confidence interval for the probability the competent-face method will work
was calculated to be 0.72 ± 2(0.09) . Based on your confidence interval, we can conclude that the
probability the competent-face method will work is greater than 50%.
a) True
b) False
Answer: A. True
Question 10: If you are concerned that the validity conditions aren't met, use a theory-based approach
to compute a confidence interval for the mean.
a) True
b) False
Answer: B. False
Question 11: Suppose a 95% confidence interval for a population proportion is found using the 2SD or
theory-based method. Which of the following will definitely be contained in that interval?
a) The p-value
b) The population proportion
c) The sample proportion
Answer: C. The sample proportion
Question 12: A recent Gallup poll showed the president's approval rating at 60%. Some friends use this
information (along with the sample size from the poll) and find theory-based confidence intervals for
the proportion of all adult Americans that approve of the presidents approve of the president's
performance. Of the following four confidence intervals, identify the ones that were definitely done
incorrectly. (There may be more than term-12one interval that is incorrect.)
a. (0.57, 0.63)
b. (0.58, 0.62)
c. (0.60, 0.66)
d. (0.47, 0.53)
Answer: C. (0.60, 0.66) d. (0.47, 0.53)
Page 3
, Question 13: Based on an August 2013 Gallup poll, a 95% confidence interval for the proportion of
American adults that thought math was the most valuable subject they studied in school is 0.31 to 0.37.
Explain exactly what the confidence interval is estimating.
a) The confidence interval is estimating the proportion of all respondents to the poll that thought math was the
most valuable subject they studied in school.
b) The confidence interval is estimating the mean of all American adults that thought math was the most
valuable subject they studied in school.
c) The confidence interval is estimating the mean of all respondents to the poll that thought math was the most
valuable subject they studied in school.
d) The confidence interval is estimating the proportion of all American adults that thought math was the most
valuable subject they studied in school.
Answer: D. The confidence interval is estimating the proportion of all American adults that thought math
was the most valuable subject they studied in school.
Question 14: According to the 95% confidence interval:
a) There is not convincing evidence that less than half of SLO residents dine at restaurants at least once a week,
because the interval does not contain 0.50.
b) There is convincing evidence that less than half of SLO residents dine at restaurants at least once a week,
because the interval does not contain 0.50.
c) Neither of the other choices is correct.
Answer: B. There is convincing evidence that less than half of SLO residents dine at restaurants at least
once a week, because the interval does not contain 0.50.
Question 15: What proportion of San Luis Obispo (SLO) residents dine at restaurants at least once a
week? To investigate, a local high school student, Deidre, decides to conduct a survey. She selects a
random sample of adult residents of SLO, asks each participant whether he/she dines at restaurants at
least once a week, and records their responses. Then, she uses her data to find a 95% confidence
interval for the proportion of SLO adults who dine out at least once a week to be (0.38, 0.44). The 99%
confidence interval based on the same data would be:
a) Wider, because to be more confident we need to widen the interval.
b) We need more information to answer this.
c) Narrower, because the more confident we are the narrower the interval.
Answer: A. Wider, because to be more confident we need to widen the interval.
Question 16: Suppose a 95% confidence interval is constructed from a sample proportion and 0.50 is
contained in the interval. Which of the following are true?
a) A 99% confidence interval constructed from the same sample proportion will definitely NOT contain 0.50.
b) A 99% confidence interval constructed from the same sample proportion will definitely contain 0.50.
c) A 90% confidence interval constructed from the same sample proportion will definitely NOT contain 0.50.
d) A 90% confidence interval constructed from the same sample proportion will definitely contain 0.50.
Answer: B. A 99% confidence interval constructed from the same sample proportion will definitely contain
0.50.
Page 4
(Grade A+)
Question 1: Random sampling is a more important consideration than random assignment if the
research question is whether students tend to receive higher scores on essays if they are encouraged to
submit a draft than if they are not so encouraged.
a) true
b) false
Answer: B. false
Question 2: Random sampling is a more important consideration than random assignment if the
research question is whether faculty tend to drive older cars than students drive on your campus.
a) true
b) false
Answer: A. true
Question 3: A randomized experiment allows for the possibility of drawing a cause-and-effect
conclusion between _________ and ________.
Answer: the explanatory and the response variable
Question 4: Which of the following must happen in a study to allow us to determine cause and effect?
Answer: Randomly assigning the observational units to different treatment groups
Question 5: One of the authors came across an article (USA Today, 2008) that said that on average
Americans have visited 16 states in the United States. Recall that in the author's sample of 50 students
the average number of states the students had visited was 9.48 and the standard deviation was 7.13. The
data are not strongly skewed. The 95% confidence interval for the average number of states all
students at the author's school have visited is (7.4537, 11.5063). Judge the validity of the following
statement: The 95% confidence interval that you calculated provides evidence that the average number
of states all students at the author's school have visited is different from 16.
a) True
b) False
Answer: A. true
Page 1
,Question 6: An instructor selected a random sample of students in her school and asked them how
many hours per week they expected to spend studying for their courses outside of class. The sample
average was 7.00 hours and the sample standard deviation was 4.19 hours. The data were not strongly
skewed. The theory-based 95% confidence interval for the parameter of interest was 5.6030 and 8.3970.
Judge the correctness of the following interpretation: We are 95% confident that the average
hours/week all students in this school will spend studying is between 5.6030 and 8.3970.
a) Not correct
b) Correct
Answer: B. Correct
Question 7: According to a 2011 report by the United States Department of Labor, civilian Americans
spend 2.75 hours per day watching television. A faculty researcher, Dr. Sameer, at California
Polytechnic State University (Cal Poly) conducts a study to see whether a different average applies to
Cal Poly students. Suppose that for a random sample of 100 Cal Poly students, the mean and standard
deviation of hours per day spent watching TV turns out to be 3.01 and 1.97 hours, respectively. The
data were used to find a 95% confidence interval: (2.619, 3.401) hours/day. Suppose that the data had
actually been collected from a sample of 150 students, and not 100, but everything else (mean and SD)
was the same as reported earlier. How, if at all, would the new 95% confidence interval based on these
data differ from the interval mentioned earlier: (2.619, 3.401) hours?
a) More information is needed to answer this question.
b) The new interval would be wider than (2.619, 3.401) hours, because the sample size is bigger.
c) The new interval would still be (2.619, 3.401) hours, because we are still 95% confident.
d) The new interval would be narrower than (2.619, 3.401) hours, because the sample size is bigger.
Answer: D. The new interval would be narrower than (2.619, 3.401) hours, because the sample size is
bigger.
Question 8: To estimate the proportion of city voters who will vote for the Republican candidate in the
election, two students, Manny and Nina, each decide to conduct polls in the city. Manny selects a
random sample of 50 voters, while Nina selects a random sample of 100 voters. Suppose both samples
result in 48% of the voters saying they will vote for the Republican candidate. Whose 95% confidence
interval will have the larger margin of error: Manny's or Nina's? How are you deciding?
a) Manny's; a small sample size will result in more variability and hence a wider interval.
b) Nina's; a large sample size will result in more variability and hence a wider interval. c)Neither; the sample
size does not affect the margin of error.
Answer: A. Manny's; a small sample size will result in more variability and hence a wider interval.
Page 2
,Question 9: A 2SD 95% confidence interval for the probability the competent-face method will work
was calculated to be 0.72 ± 2(0.09) . Based on your confidence interval, we can conclude that the
probability the competent-face method will work is greater than 50%.
a) True
b) False
Answer: A. True
Question 10: If you are concerned that the validity conditions aren't met, use a theory-based approach
to compute a confidence interval for the mean.
a) True
b) False
Answer: B. False
Question 11: Suppose a 95% confidence interval for a population proportion is found using the 2SD or
theory-based method. Which of the following will definitely be contained in that interval?
a) The p-value
b) The population proportion
c) The sample proportion
Answer: C. The sample proportion
Question 12: A recent Gallup poll showed the president's approval rating at 60%. Some friends use this
information (along with the sample size from the poll) and find theory-based confidence intervals for
the proportion of all adult Americans that approve of the presidents approve of the president's
performance. Of the following four confidence intervals, identify the ones that were definitely done
incorrectly. (There may be more than term-12one interval that is incorrect.)
a. (0.57, 0.63)
b. (0.58, 0.62)
c. (0.60, 0.66)
d. (0.47, 0.53)
Answer: C. (0.60, 0.66) d. (0.47, 0.53)
Page 3
, Question 13: Based on an August 2013 Gallup poll, a 95% confidence interval for the proportion of
American adults that thought math was the most valuable subject they studied in school is 0.31 to 0.37.
Explain exactly what the confidence interval is estimating.
a) The confidence interval is estimating the proportion of all respondents to the poll that thought math was the
most valuable subject they studied in school.
b) The confidence interval is estimating the mean of all American adults that thought math was the most
valuable subject they studied in school.
c) The confidence interval is estimating the mean of all respondents to the poll that thought math was the most
valuable subject they studied in school.
d) The confidence interval is estimating the proportion of all American adults that thought math was the most
valuable subject they studied in school.
Answer: D. The confidence interval is estimating the proportion of all American adults that thought math
was the most valuable subject they studied in school.
Question 14: According to the 95% confidence interval:
a) There is not convincing evidence that less than half of SLO residents dine at restaurants at least once a week,
because the interval does not contain 0.50.
b) There is convincing evidence that less than half of SLO residents dine at restaurants at least once a week,
because the interval does not contain 0.50.
c) Neither of the other choices is correct.
Answer: B. There is convincing evidence that less than half of SLO residents dine at restaurants at least
once a week, because the interval does not contain 0.50.
Question 15: What proportion of San Luis Obispo (SLO) residents dine at restaurants at least once a
week? To investigate, a local high school student, Deidre, decides to conduct a survey. She selects a
random sample of adult residents of SLO, asks each participant whether he/she dines at restaurants at
least once a week, and records their responses. Then, she uses her data to find a 95% confidence
interval for the proportion of SLO adults who dine out at least once a week to be (0.38, 0.44). The 99%
confidence interval based on the same data would be:
a) Wider, because to be more confident we need to widen the interval.
b) We need more information to answer this.
c) Narrower, because the more confident we are the narrower the interval.
Answer: A. Wider, because to be more confident we need to widen the interval.
Question 16: Suppose a 95% confidence interval is constructed from a sample proportion and 0.50 is
contained in the interval. Which of the following are true?
a) A 99% confidence interval constructed from the same sample proportion will definitely NOT contain 0.50.
b) A 99% confidence interval constructed from the same sample proportion will definitely contain 0.50.
c) A 90% confidence interval constructed from the same sample proportion will definitely NOT contain 0.50.
d) A 90% confidence interval constructed from the same sample proportion will definitely contain 0.50.
Answer: B. A 99% confidence interval constructed from the same sample proportion will definitely contain
0.50.
Page 4
