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13th Edition

Anderson

Publisher: CENGAGE L

ISBN: 9781305881884

Chapter 9.5, Problem 39E

Textbook Problem

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What percentage of the population live in their state of birth? According to the U.S. Census Bureau’s American Community Survey, the figure ranges from 25% in Nevada to 78.7% in Louisiana (*AARP Bulletin,* March 2014). The average percentage across all states and the District of Columbia is 57.7%. The data in the DATAfile Homestate are consistent with the findings in the American Community Survey. The data are for a random sample of 120 Arkansas residents and for a random sample of 180 Virginia residents.

- a. Formulate hypotheses that can be used to determine whether the percentage of stay-at-home residents in the two states differs from the overall average of 57.7%.
- b. Estimate the proportion of stay-at-home residents in Arkansas. Does this proportion differ significantly from the mean proportion for all states? Use
*α =*.05. - c. Estimate the proportion of stay-at-home residents in Virginia. Does this proportion differ significantly from the mean proportion for all states? use
*α*= .05. - d. Would you expect the proportion of stay-at-home residents to be higher in Virginia than in Arkansas? Support your conclusion with the results obtained in parts (b) and (c).

**a.**

To determine

Identify the null and alternative hypotheses most appropriate for the given situation.

Here, the claim is that the percentage of stay-at-home residents in the two states differs from the overall average of 57.7%. This can be written as

**b.**

To determine

Find the proportion of stay-at-home residents in Arkansas.

Check whether the proportion differ significantly from the mean proportion for all states or not.

**c.**

To determine

Find the proportion of stay-at-home residents in Virginia.

Check whether the proportion differ significantly from the mean proportion for all states or not.

**d.**

To determine

Explain the proportion of stay-at-home residents to be higher in Virginia than in Arkansas.

STATISTICS F/BUSINESS+ECONOMICS-TEXT

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