Question

In a survey of 390390 childless married couples who were asked if they plan to have children in the next 55 years, 13%13% of the men and 16%16% of the women responded "Yes". Based on this survey, can it be concluded that there is a difference in the proportion of men ( p1p1 ) and women ( p2p2 ) responding "Yes"? Use a significance level of α=0.1α=0.1 for the test.

Step 4 of 5 :  

Find the P-value for the hypothesis test. Round your answer to four decimal places.

Answer 1

Answer:

Given,

p1^ = 0.13

p2^ = 0.16

Pooled proportion pbar = (n1p1^ + n2p2^)/(n1+n2)

substitute values

= (390*0.13 + 390*0.16)/(400+400)

= 0.1414

Null hypothesis Ho : p1 = p2

Alternative hypothesis Ha : p1 != p2

test statistic z = (p1^ - p2^)/sqrt(p(1-p)*(1/n1 + 1/n2))

substitute values

= (0.13 - 0.16)/sqrt(0.1414(1-0.1414)*(1/400 + 1/400))

z = -1.22

|z| = 1.22

Corresponding p value = P(z < -1.22) [two tailed

= 0.2224649 [since from z table]

= 0.2225

Here we observe that, p value > alpha, so we fail to reject Ho,so there is no difference in the proportion of men (p1 ) and women (p2 )