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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 18–29play 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 18–29 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

Age and September 11 Refer to Exercise 42. The study also reported that 86% of

millennials included 9/11 in their top-10 list and 70% of baby boomers included 9/11.

a. Explain why you do not have enough information to give confidence intervals for

millennials and baby boomers separately.

b. Do you think a 95%confidence interval for baby boomers would have a larger or smaller margin of error than the estimate from Exercise 42? Explain your answer.

You have an SRS of 23observations from a large population. The distribution of sample values is roughly symmetric with no outliers. What critical value would you use to obtain a 98%confidence interval for the mean of the population?

a. 2.177

b. 2.183

c. 2.326

d. 2.500

e. 2.508

California’s traffic People love living in California for many reasons, but traffic isn’t one of them. Based on a random sample of 572employed California adults, a 90%confidence interval for the average travel time to work for all employed California adults is 23minutes to 26 minutes.

a. Interpret the confidence level.

b. Name two things you could do to reduce the margin of error. What drawbacks do these actions have?

c. Describe how non response might lead to bias in this survey. Does the stated margin of error account for this possible bias?

One reason for using a t distribution instead of the standard Normal distribution to find critical values when calculating a level C confidence interval for a population mean is that

a. zcan be used only for large samples.

b. zrequires that you know the population standard deviation σ.

c. z requires that you can regard your data as an SRS from the population.

d. z requires that the sample size is less than 10% of the population size.

e. a z critical value will lead to a wider interval than a t critical value.

Shoes The AP Statistics class in Exercise 1 also asked an SRS of 20boys at their school how many pairs of shoes they have. A 95%confidence interval for μG-μB=the true difference in the mean number of pairs of shoes for girls and

boys is 10.9to26.5.

a. Interpret the confidence interval.

b. Does the confidence interval give convincing evidence of a difference in the true mean number of pairs of shoes for boys and girls at the school? Explain your answer.
See all solutions

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