Question

A survey of 500 randomly chosen adults found that
30% of the 300 men and 20% of the 200 women had purchased books online.
You are to test the hypothesis that online rates are the same for men and women.
What is the p-value of your test of significance?

Answer 1

Pooled proportion p = (p1 * n1 + p2 * n2) / ( n1 + n2)

= (0.30 * 300 + 0.20 * 200) / ( 300 + 200)

= 0.26

Test statistics

z = (p1 - p2) / Sqrt ( p ( 1 -p ) * (1 / n1 + 1 / n2) )

= 0.30 - 0.20 / sqrt (0.26 * 0.74 * ( 1 / 300 +1 / 200) )

= 2.50

This is test statistics value.

p-value for two tailed test is

p-value = 2 * P( Z >z)

= 2 * P( Z > 2.50)

= 2 * 0.0062

= 0.0124