A difference of proportions

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In a poll, 350 of 980 women and 420 of 1108 men said they would vote for a given candidate. Give a 90% confidence interval for the difference between the women’s proportion and the men’s proportion. Use z_{0.95}=1.645.

Worked answer (click to show)

\widehat p_W=350/980=0.3571 and \widehat p_M=420/1108=0.3791. The difference is -0.0219 and the estimated standard error is 0.0211. Then

-0.0219\pm 1.645\times 0.0211=(-0.057,\,0.013).