Question

Researchers are interested in determining whether more men than women prefer beef to chicken. In a random sample of 250 men, 75% prefer beef, whereas in a random sample of 350 women, 55% prefer beef. What is the 95% confidence interval estimate for the difference between the percentages of men and women who prefer beef over chicken?

Answer 1

n1 = 250

p1 = 0.75

n2 = 350

p2 = 0.55

Q= 1 - P =0.3667

= 0.05

From Table, critical values of Z = 1.96

Confidence interval:

(0.75 - 0.55) (1.96 X 0.04)

= 0.20 0.0785

= ( 0.1215 ,0.2785)

So

Confidence interval:

0.1215 < P1 - P2 < 0.2785