Question

A group of researchers want to determine if there are any significant differences in marital satisfaction between male and female spouses. To test this hypothesis, they collected data on marital satisfaction from 28 couples (i.e., 28 men and 28 women). They observed that the average marital satisfaction among men was 6.5, and the average among women was 6.0. The sum of squares for the difference scores (SSD) was 440. Additionally, male and female spouse marital satisfaction were strongly related (r = .51). Use a confidence interval (where α = .01) to determine if there is a significant difference in marital satisfaction between male and female spouses. A group of researchers want to determine if there are any significant differences in marital satisfaction between male and female spouses. To test this hypothesis, they collected data on marital satisfaction from 28 couples (i.e., 28 men and 28 women). They observed that the average marital satisfaction among men was 6.5, and the average among women was 6.0. The sum of squares for the difference scores (SSD) was 440. Additionally, male and female spouse marital satisfaction were strongly related (r = .51). Use a confidence interval (where α = .01) to determine if there is a significant difference in marital satisfaction between male and female spouses.

Answer 1

The following needs to be tested:

where corresponds to the population correlation.

The sample size is n=28, so then the number of degrees of freedom is

The corresponding critical correlation value ​ for a significance level of , for a two-tailed test is:

Observe that in this case, the null hypothesis is rejected if

Based on the sample correlation provided, we have that , from which is concluded that the null hypothesis is rejected. and there is a significant difference in marital satisfaction between male and female spouses.