Question

In a CBS News survey done in 2000, 92% of n = 620 randomly sampled married men said that they would marry their spouses again if they had it to do all over again. In the same survey, 90% of n = 697 married women said that they would marry their spouses if they had it to do all over again. Test if the proportions differ for each gender.

Answer 1

To test if the proportions of married men and married women who would marry their spouses again differ, we can use a two-sample proportion test.

Step-by-step explanation:

To test if the proportions of married men and married women who would marry their spouses again differ, we can use a two-sample proportion test.

1. Hypotheses: The null hypothesis (H0) is that the proportions are equal and the alternative hypothesis (Ha) is that the proportions are different.
2. Calculate the test statistic: We can use the formula for the test statistic: Z = (p1 - p2) / sqrt(p*(1-p)*(1/n1 + 1/n2)), where p1 and p2 are the proportions of married men and married women who would marry their spouses again, and p is the pooled proportion.
3. Calculate the p-value: Using the test statistic, we can calculate the p-value by comparing it to the standard normal distribution.
4. Make a conclusion: If the p-value is less than the chosen significance level (usually 0.05), we reject the null hypothesis and conclude that the proportions differ.