Question

A random sample of 124 women over the age of 15 found that 3.68% of them have been divorced. A random sample of 290 men over the age of 15 found that 5.86% have been divorced. Assuming normality and using a 95% significance level, test the claim that the proportion of divorced women is different than the proportion of divorced men.

For this scenario, provide a hypothesis test with all six steps and provide both the critical value and the p-value.

provide a confidence interval estimate of the true difference in proportions between men and women who have been divorced.   

Explain how your hypothesis test in 12 and your confidence interval in 13 are consistent.

Answer 1

Let p denotes the true proportion of divorced men over the age 15.

i)

ii)

Since the confidence interval does not includes 0.368, so at 95% level of confidence or at 5% level of significance, we can conclude that there is not sufficient evidence to support the claim that the proportion of divorced women is different than the proportion of divorced men.