2. T-test for dependent means You want to see if completion of PSY-3205 has changed the overall happiness for students taking the class. In order to do this, you do a repeated measures happiness survey like that described above where you survey a group of N = 4 students before they take the class and survey these same students they take the class.

You obtain the following data:

Student; Happiness Before; Happiness After
1; 4; 2
2; 7; 3
3; 5; 4
4; 4; 1

Let D = (Happiness After) – (Happiness Before) denote your difference score

a) State the null hypothesis (H0) and the research hypothesis (H1)

b) Compute the mean difference score MD

c) Compute the degrees of freedom (df)

d) Fill out the following table and then estimate the standard deviation (sD) of difference scores

D (D-MD) (D-MD)2


SSD :

e) Write the expression for your T-statistic, and plug in the numbers to compute the t-score

f) Using the attached T-score table, for a 2-tailed test is your observation significant at the level of p<0.05? How about p < 0.01?

g) Compute Cohen’s d

h) What is the 95% confidence interval for the true difference? Does it contain zero?