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For Exercise 3.1, see page 47; for Exercise 3.2, see page 49.
3.3 What’s the parameter? An online store contacts 1500 customers from its list of customers who have purchased in the last year and asks the customers if they are very satisfied with the store’s website. One thousand (1000) customers respond, and 696 of the 1000 say that they are very satisfied with the store’s website. The parameter is
(a) the 69.6% of respondents who replied they are very satisfied with the store’s website.
(b) the percentage of the 1500 customers contacted who would have replied they are very satisfied with the store’s website.
(c) the percentage of all customers who purchased in the last year who would have replied they are very satisfied with the store’s website.
(d) None of the above is the parameter.
3.4 What’s the statistic? A state representative wants to know how voters in his district feel about enacting a statewide smoking ban in all enclosed public places, including bars and restaurants. His staff mails a questionnaire to a simple random sample of 800 voters in his district. Of the 800 questionnaires mailed, 152 were returned. Of the 152 returned questionnaires, 101 supported the enactment of a statewide smoking ban in all enclosed public places. The statistic is
(a) 152800 = 19.0%
(b) 101800 = 12.6%
(c) 101152 = 66.4%
(d) unable to be determined based on the information provided.
3.5 Decreasing sampling variability. You plan to take a sample of size 500 to estimate the proportion of students at your school who support having no classes and special presentations on Veteran’s Day. To be twice as accurate with your results, you should plan to sample how many students? (Hint: Use the quick and approximate method for the margin of error.)
(a) 125 students
(b) 250 students
(c) 1000 students
(d) 2000 students
3.6 What can we be confident about? A May 2015 University of Michigan C.S. Mott Children’s Hospital National Poll on Children’s Health reported that 90% of adults are concerned that powdered alcohol will be misused by people under age 21. The margin of error was reported to be 2 percentage points, and the level of confidence was reported to be 95%. This means that
(a) we can be 95% confident that between 88% and 92% of adults are concerned that powdered alcohol will be misused by people under age 21.
(b) we can be 95% confident that between 88% and 92% of adults who were surveyed are concerned that powdered alcohol will be misused by people under age 21.
(c) we know that 90% of adults are concerned that powdered alcohol will be misused by people under age 21.
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(d) Both (a) and (b) above are true.
3.7 Which is more accurate? The Pew Research Center Report entitled “How Americans value public libraries in their communities,” released December 11, 2013, asked a random sample of 6224 Americans aged 16 and older, “Have you used a Public Library in the last 12 months?” In the entire sample, 30% said Yes. But only 17% of those in the sample over 65 years of age said Yes. Which of these two sample percents will be more accurate as an estimate of the truth about the population?
(a) The result for those over 65 is more accurate because it is easier to estimate a proportion for a small group of people.
(b) The result for the entire sample is more accurate because it comes from a larger sample.
(c) Both are equally accurate because both come from the same sample.
(d) We cannot determine this, because we do not know the percentage of those in the sample 65 years of age or younger who said Yes.