The following is computer output from a statistical analysis comparing married and never married study subjects with respect to the means of the Life Purpose and Satisfaction variable. Examine the output and answer the following:

    1. State the null and alternative hypotheses for the study.
    1. Which of the two t-test methods would you use, equal variance or unequal variance t-test? (Concisely explain your choice)
    1. Is the difference statistically significant? (What can you point to in the output that tells you this?)

Solution: (a) Our hypotheses are:

(b) We have to use the method that assumes equal variance because the p-value for the equality of variances is 0.712, which is greater than the level of significance 0.05. That means that we can assume equal variances.

(c) The table shows that the p-value is 0.007, which is less than the significance level 0.05, and therefore, we reject the null hypothesis. Therefore the difference is significant.