Difference in support rates between two groups

Question

In a survey, 260 of 400 women support a proposal, compared with 220 of 400 men. Construct a 95% confidence interval for the difference in support rates (women minus men), and state your conclusion.

Accepted Answer

Setup. Use (\hat{p}W - \hat{p}M) \pm z^{}\sqrt{\hat{p}W(1-\hat{p}W)/nW + \hat{p}M(1-\hat{p}M)/nM} with z^{} = 1.96. Here \hat{p}W = 0.65, \hat{p}M = 0.55, difference = 0.10. Compute the standard error. \sqrt{\frac{0.65 	imes 0.35}{400} + \frac{0.55 	imes 0.45}{400}} = \sqrt{0.00056875 + 0.00061875} = \sqrt{0.0011875} = 0.0345. Margin of error = 1.96 	imes 0.0345 = 0.0675, so 0.10 \pm 0.0675 = [0.032,\ 0.168]. Interpret. The interval lies entirely above zero, so women's support is significantly higher than men's at the 5% level, by roughly 3 to 17 points. Takeaway. Larger samples (400 per g…

Difference in support rates between two groups

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