Question

To do so you randomly surveyed 1000 men and 1200 women. 100 men responded that they were members of the Tea Party. 95 women responded that they were members of the Tea Party. Find the two-tailed p-value for this hypothesis test.

Answer 1

The two-tailed p-value for the hypothesis test is 0.101.

Explanation:

Test statistic (z) = (p1 - p2) ÷ sqrt[p(1-p)(1/n1 + 1/n2)]

p1 is sample proportion of men = 100/1000 = 0.1

p2 is sample proportion of women = 95/1200 = 0.08

n1 is sample size of men = 1000

n2 is sample size of women = 1200

p is pooled proportion of men and women = (n1p1 + n2p2) ÷ (n1 + n2) = (1000×0.1 + 1200×0.08) ÷ (1000 + 1200) = 0.089

z = (0.1 - 0.08) ÷ sqrt[0.089(1-0.089)(1/1000 + 1/1200)] = 0.02 ÷ 0.0122 = 1.64

The cumulative area of test y is obtained from the normal distribution table by taking the value of 1.6 under 0.04. The value of the cumulative area is 0.9495

Two-tailed p-value = 2(1 - 0.9495) = 2×0.0505 = 0.101