Hypothesis test (t-statistic) and now testing the effect size with r2:

r² = t² / t² + df = (4.79)² / (4.79)² + 9 = 22.976 / 22.976 + 9 = 22.976 / 31.976 = 0.7185

Can you help me explain the conclusion? Essentially that 71.85% of the variance in the scores is explained by...?

I included additional information below if you need it. I bolded and underlined the section I need help with. Thank you!!

Question 5 (17 points)

After conducting your study in Question 4 above, you wanted to determine if the higher social class participants would significantly change their scores following volunteer work with a charitable organization for half a year. You re-tested them on the same test after volunteering. Was there a significant difference in their empathy and social support scores after volunteering? Using the five steps of hypothesis testing, test at .05, one-tailed test. If the difference is significant, test the effect size through r2 and describe the effect size.

Particpant	After Volunteering	Before Volunteering	D	D2
A B C D E F G H I J	15 13 19 18 10 14 14 15 14 18	10 10 17 12 10 11 13 10 12 16	5 3 2 6 0 3 1 5 2 2	25 9 4 36 0 9 1 25 4 4
D = 29 D2 = 117 MD = 29/10 = 2.9 SS= D2 - (D)2/n = 117 - (29)2/10 = 117-841/10 = 117-84.1 = 32.9

Step 1. State the hypotheses and select the alpha level H₀: _D 0 (there is no increase following volunteer work) H₁: _D > 0 (empathy and social support scores are increased)

For this test, we use = .05, one-tailed

Step 2. Locate the critical region Look at the sample mean difference to verify that it is in the predicted direction. If not, then treatment (volunteering) did not work. I see that M_D = 2.9, so the change is in the correct direction (scores increased).

With n=10, we obtain df=9, and a critical value of t= 1.833 for a one-tailed test with = .05.

Step 3. Compute the t statistic Sample variance = s² = SS/n-1 = 32.9 / 9 = 3.66

Estimated standard error = s_MD =s2n=3.6610 = 0.366 = 0.605

t statistic = t = M_D - _D / s_MD= 2.9 - 0 / 0.605 = 4.79

Step 4. Make a decision Since the t-value we obtained (+4.79) is beyond the critical region of +1.833, H₀ will be rejected.

Step 5. Conclusion Based on the t-value we obtained, we can conclude that volunteering increased empathy and social support scores in higher-class participants.