A researcher is studying differences in voter turnout between men and women. Let

Question

A researcher is studying differences in voter turnout between men and women. Let p1 and p2 be, respectively, the fraction of eligible male and female voters who cast a ballot in the last election.

a. The researcher started out by polling 100 eligible voters of each gender and found that 55 of the men and 60 of the women had cast a ballot. Construct a 95% confidence interval for the difference in voter turnout rates by gender.

b. If the researcher wants the sampling error for the confidence interval to be less than ±0.1, and wants the two samples to have equal size, how many men and women does she need to poll to guarantee this result?

c. If the sample size of women is fixed at n2 = 100 . How many men would the researcher need to poll to achieve a sampling error of less than ±0.1? (d) If the sample size of women is fixed at n2 = 100 . How many men would the researcher need to poll to achieve a sampling error of less than ±0.05?

Explanation / Answer

A researcher is studying differences in voter turnout between men and women. Let

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