A study 17 compared personality characteristics between 49 children of alcoholics and a control group of 49 children of non-alcoholics who were matched on age and gender. On a measure of wellbeing, the 49 children of alcoholics had a mean of 26.1 (s = 7.2) and the 49 subjects in the control group had a mean of 28.8 (s = 6.4). The difference scores between the matched subjects from the two groups had a mean of 2.7 (s = 9.7).
a. Are the groups to be compared independent samples or dependent samples? Why?
b. Show all steps of a test of equality of the two population means for a two-sided alternative hypothesis. Report the P-value and interpret.
c. What assumptions must you make for the inference in part b to be valid?