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Chapter 8: Q. 15 (page 483)

The AP Statistics class in Exercise 1 also asked an SRS of 20 boys at their school how many shoes they have. A 95% confidence interval for the difference in the population means (girls 鈥� boys) is 10.9 to 26.5. Interpret the confidence interval and the confidence level.

Short Answer

Expert verified

Interpretation confidence level: The confidence interval contains the true difference in population means, on average, in 95%of all samples.

Step by step solution

01

Given Information

A 95% confidence interval for the difference in the population means (girls 鈥� boys) is 10.9 to26.5.

02

Explanation

The given 95%confidence interval for the difference in population means is 10.9to 26.5.

Interpretation: We are 95%confident that the difference in the population means between girls and boys is between 10.9and 26.5.

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Most popular questions from this chapter

Bone loss by nursing mothers.: Breastfeeding mothers secrete calcium into their milk. Some of the calcium may come from their bones, so mothers may lose bone minerals. Researchers measured the per cent change in bone mineral content (BMC) of the spines of 47randomly selected mothers during three months of breastfeeding. The mean change in BMC was 3.587%and the standard deviation was 2.506%.

(a) Construct and interpret a 99% confidence interval to estimate the mean per cent change in BMC in the population.

(b) Based on your interval from (a), do these data give good evidence that on average nursing mothers lose bone minerals? Explain

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49. A Gallup Poll found that only 28%of American adults expect to inherit money or valuable possessions from a relative. The poll鈥檚 margin of error was 卤3percentage points at a 95% confidence level. This means that
(a) the poll used a method that gets an answer within 3%of the truth about the population 95% of the time.
(b) the percent of all adults who expect an inheritance is between 25%and 31%.
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The U.S. Forest Service is considering additional restrictions on the number of vehicles allowed to enter Yellowstone National Park. To assess public reaction, the service asks a random sample of 150 visitors if they favour the proposal. Of these, 89 say 鈥淵es.鈥�

(a) Construct and interpret a 99% confidence interval for the proportion of all visitors to Yellowstone who favours the restrictions.

(b) Based on your work in part (a), can the U.S. Forest Service conclude that more than half of visitors to Yellow-stone National Park favour the proposal? Justify your answer.

Do you go to church? The Gallup Poll plans to ask a random sample of adults whether they attended a religious service in the last 7days. How large a sample would be required to obtain a margin of error of 0.01ina99%confidence interval for the population proportion who would say that they attended a religious service? Show your work.

- Construct and interpret a confidence interval for a population proportion.

- Explain how practical issues like nonresponse, under coverage, and response bias can affect the interpretation of a confidence interval.
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