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Chapter 8: Q 43. (page 523)

Age and video games Refer to Exercise 41. The study also estimated that 67% of adults aged 18鈥�29play video games, but only 25%of adults aged 65and older play video games.

a. Explain why you do not have enough information to give confidence intervals for these two age groups separately.

b. Do you think a 95% confidence interval for adults aged 18鈥�29 would have a larger or smaller margin of error than the estimate from Exercise 41? Explain your answer.

Short Answer

Expert verified

a. Sample sizes are unknown and sample proportions are given. It is not possible to give confidence levels.

b. It would have larger margin of error than estimate.

Step by step solution

01

Given Information

Sample size is decreasing and adults in sample is less than all individuals.

02

Why we do not have enough information to give confidence intervals for two age groups separately.

We should have knowledge of sample proportion and sample size to construct confidence interval. So, we do not have enough information to give confidence intervals for two age groups separately.

03

To check if 95% confidence interval for adults would have smaller or larger margin of error than estimate.

As number of adults are less than that in sample, we are decreasing sample size.

We have less information about population and less accurate estimates are obtained. Hence, estimate is far from true value and confidence interval has to be wider. Margin of error is larger as it is half of confidence interval.

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Most popular questions from this chapter

Check them all Determine if the conditions are met for constructing a confidence interval for the population mean in each of the following settings.

a. How much time do students at your school spend on the Internet? You collect data from the 32members of your AP Statistics class and calculate the mean amount of time that these students spent on the Internet yesterday.

b. Is the real-estate market heating up? To estimate the mean sales price, a realtor in a large city randomly selected 100home sales from the previous 6months in her city. These sales prices are displayed in the boxplot.

The researcher is deciding between a 95% confidence level and a 99% confidence level. Compared with a 95% confidence interval, a 99% confidence interval will be

a. narrower and would involve a larger risk of being incorrect.

b. wider and would involve a smaller risk of being incorrect.

c. narrower and would involve a smaller risk of being incorrect.

d. wider and would involve a larger risk of being incorrect.

e. wider and would have the same risk of being incorrect.

Teens and their TV sets According to a Gallup Poll report, 64%of teens aged 13to 17have TVs in their rooms. Here is part of the footnote to this report:

These results are based on telephone interviews with a randomly selected national sample of 1028teenagers in the Gallup Poll Panel of households, aged 13to 17. For results based on this sample, one can say that the maximum error attributable to sampling and other random effects is 卤3percentage points. In addition to sampling error, question wording and practical difficulties in conducting surveys can introduce error or bias into the findings of public opinion polls.

a. We omitted the confidence level from the footnote. Use what you have learned to estimate the confidence level, assuming that Gallup took an SRS.

b. Give an example of a 鈥減ractical difficulty鈥� that could lead to bias in this survey.

A plethora of pepperoni? Refer to Exercise 73.

a. Explain why it was necessary to inspect a graph of the sample data when checking the Normal/Large Sample condition.

b. According to the manager of the restaurant, there should be an average of 40

pepperonis on a large pizza. Based on the interval, is there convincing evidence that the average number of pepperonis is less than 40? Explain your answer.

10Bottling cola A particular type of diet cola advertises that each can contains 12 ounces of the beverage. Each hour, a supervisor selects cans at random, measures their contents, and computes a 95%confidence interval for the true mean volume. For one particular hour, the 95%confidence interval is 11.97ounces to 12.05ounces.

a. Does the confidence interval provide convincing evidence that the true mean volume is different than 12ounces? Explain your answer.

b. Does the confidence interval provide convincing evidence that the true mean volume is 12ounces? Explain your answer.
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