Question

One of the benefits of aerobic exercise is the release of endorphins, which are natural chemicals in the brain that produce a feeling of general well-being. A sample of n = 20 subjects was obtained, and each person's tolerance for pain was tested before and after a 50-minute session of aerobic exercise. On average, the pain tolerance for this sample is MD = -13.46 points (D = X1 - X2) with pain tolerance higher after exercise than before. The SS for the sample of difference scores is SS = 968.00. Do these data indicate a significant increase in pain tolerance following exercise. Use a one-tailed test with α = .05. Questions 20-34 are for this study.

What is the variance (sp2 or s2) value for this analysis?

Hint: You use pooled variance (s2p) if you are completing an independent samples t-test, and you use the variance value (s2) for a repeated measures t-test.

s subscript p superscript 2 equals fraction numerator S S subscript 1 plus S S subscript 2 over denominator d f subscript 1 plus d f subscript 2 end fraction equals fraction numerator S S subscript 1 plus S S subscript 2 over denominator left parenthesis n subscript 1 minus 1 right parenthesis plus left parenthesis n subscript 2 minus 1 right parenthesis end fraction s squared equals fraction numerator S S over denominator d f end fraction equals fraction numerator S S over denominator left parenthesis n minus 1 right parenthesis end fraction

a. 48.40

b. 50.95

c. 222.07

d. 216.45

Answer 1

Given that, sample size ( n ) = 20

The Sum of square ( SS ) for the sample of difference scores is SS = 968.00

We want to find, sample variance ( S² )

S² = SS / (n - 1) = 968.00 / (20 - 1) = 968.00/19 = 50.95

=> S² = 50.95

Answer: b) 50.95