Question

In a survey of 340340 childless married couples who were asked if they plan to have children in the next 55 years, 30%30% of the men and 27%27% 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=0.05α=0.05 for the test.

1. State the null and alternative hypotheses for the test.

2. Compute the weighted estimate of p, -p

3. Make the decision to reject or fail to reject the null hypothesis.

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

5. Make the decision to reject or fail to reject the null hypothesis. does the evidence support or fail

4.

Answer 1

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(4) Decision about the null hypothesis

Since it is observed that |z| = 0.849 < Zc​=1.96, it is then concluded that the null hypothesis is not rejected.

5. P-value
p-value equals 0.434478, ( p(x≤Z) = 0.782761 ). This means that if we would reject H0, the chance of type I error (rejecting a correct H0) would be too high: 0.4345 (43.45%).
The larger the p-value the more it supports H0.

Since p-value > α, H0 is accepted.
The proportion of men 's population is considered to be equal to the proportion. of the women's population.
In other words, the difference between the proportion of the men and women populations is not big enough to be statistically significant.

We fail to reject the null hypothesis. Therefore, childless married couples who were asked if they plan to have children are not statistically significant in the proportion of men and women