Question

In a random sample of 360 women, 65% favored stricter gun control laws. In a random sample of 220 men, 60% favored stricter gun control laws. Test the claim that the proportion of women favoring stricter gun control is higher than the proportion of men favoring stricter gun control. Use a significance level of 0.05.

Test and CI for Two Proportions
Sample X N Sample p
1 234 360 0.65
2 132 220 0.60
Difference = p (1) - p (2)
Estimate for difference: 0.05
Test for difference = 0 (vs > 0): Z = 1.21 P-Value = 0.1129

Answer 1

Test claim is the proportion of women favoring stricter gun control is higher than the proportion of men favoring stricter gun control.

So, hypothesis is ,

H0 : P1 - P2 = 0

Ha : P1 - P2 > 0

We are given,

Test statistic = 1.21

P-value = 0.1129

Decision about null hypothesis :

Rule : Reject null hypothesis if p-value less than significance level = 0.05

It is observed that p-value ( 0.1129) is greater than = 0.05

So fail to reject null hypothesis.

Conclusion :

There is not sufficient evidence to support the claim that the proportion of women favoring stricter gun control is higher than the proportion of men favoring stricter gun control