T-test for paired samples
Suppose you have a group of patients and give them a mood questionnaire before a psychological intervention, and then you want to determine if there is a significant improvement in their mood after a psychological intervention. You have the scores before the questionnaire (Pre) and the scores after (Post) for each patient. You have the scores before the questionnaire (Pre) and the scores after (Post) for each patient. You want to test the null hypothesis that there is no difference in the scores before and after the intervention, that is, H0: mu Pre = mu Post, where mu is the mean. Null hypothesis (H0): There is no significant difference between scores before and after tutoring (mu d = 0).
Alternative hypothesis (H1): There is a significant difference between scores before and after tutoring (mu d != 0). If alpha = 0.05, t-value = 14.75 and a critical value of 2.32. By comparing the values of the t-test and the critical value, it can be concluded that: