Question

As a sociologist, you are interested in investigating the stress levels of people who live in urban versus rural areas. You randomly select 80 urban residents and 70 rural residents to interview. Respondents from urban areas experience an average of 13.2 stressful experiences per week with a standard deviation of 3.2 times. Respondents from rural areas experience an average of 11.5 stressful experiences per week with a standard deviation of 2.1 times. We set the alpha level at 0.01. Please perform the appropriate hypothesis test using five steps.

Answer 1

The test hypothesis is

This is a two-sided test because the alternative hypothesis is formulated to detect differences from the hypothesized difference in mean values on either side.

Now, the value of test static can be found out by following formula:

Using Excel's function , the P-value for t0 = 3.7873 in an t-test with 148 degrees of freedom can be computed as

We would reject the null hypothesis H_0 in favor of the alternative hypothesis H_1 because P = 0.00022 <0.01

Degrees of freedom on the t-test statistic are n1 + n2 - 2 = 80 + 70 - 2 = 148

Since t0 = 3.7873 > 2.609 = t{0.005, 148}, we reject the null hypothesis H0  in favor of the alternative hypothesis