Statistics
Sampling voters. Your state representative is planning on supporting a bill legalizing same-sex marriage in your state and wants to estimate the proportion of voters in her district who support this bill. She mails a survey to an SRS of 1300 registered voters in her district, and 800 surveys are returned. In the sample of 800 surveys returned to your state representative, 528 are from female voters.

(a)In her district, voter registration records show that 54% of the registered voters are female. If the 800 returned surveys are an SRS of registered voters, do you feel that the difference between the proportion of female voters that responded to the survey and the population proportion of 54% can be easily explained by chance variation? State the hypotheses and give the P-value. Give your conclusion in the context of the problem.

(b)Among the 800 surveys that are returned, 72% support the bill. If women are more likely to support the bill legalizing same-sex marriage than men, what would be the likely direction of the bias in the estimate of the proportion of registered voters who support the bill? Explain your answer.

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