Suppose you work for the Las Vegas Chamber of Commerce, and you want to estimate

Question

Suppose you work for the Las Vegas Chamber of Commerce, and you want to estimate with 95% confidence the difference between the percentage of all females who have ever gone to see an Elvis impersonator and the percentage of all males who have ever gone to see an Elvis impersonator, in order to help determine how you should market your entertainment offerings. Suppose your random sample of 100 females includes 53 females who have seen an Elvis impersonator and that your random sample of 110 males includes 37 males who have ever seen an Elvis impersonator.

Explanation / Answer

here p1 =53/100 =0.53 ; n1=100

p2=37/110 =0.3364 ; n2=110

therefore std error of mean difference =(p1(1-p1)/n1 +p2(1-p2)/n2)1/2 =0.0672

for 95% CI, z=1.96

hence 95% Ci of difference b/w mean proportion =(p1-p2) +/- z*std error =0.0619 ; 0.3254

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