(i) How large a sample of Kansas voters is needed if we wish to be 95% sure that

Question

(i) How large a sample of Kansas voters is needed if we wish to be 95% sure that the sample proportion of Democrats estimates the true proportion of Kansas Democrats with an error not exceeding 01? (ii) In a study to estimate the proportion of wives who regularly watch soap operas, it is found that 56 of 180 wives in Boston and 60 of 235 wives in Santa Fe watch at least one soap opera. Use a 01 level of significance to test the claim that the proportion of wives that watch soap operas in Boston is different than that in Santa Fe.

Explanation / Answer

Part-i

Sample size n>=p*(1-p)(z/ME)2=0.5*(1-0.5)*(1.96/0.01)2=9604

so n=9604

Part-ii

From following results p-value=0.209>0.01, so conclude that proportions are not different

Test and CI for Two Proportions

Sample X N Sample p
1 56 180 0.311111
2 60 235 0.255319

Difference = p (1) - p (2)
Estimate for difference: 0.0557920
99% CI for difference: (-0.0593952, 0.170979)
Test for difference = 0 (vs 0): Z = 1.26 P-Value = 0.209

Fisher’s exact test: P-Value = 0.226

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