Question: The SF36 is a psychometric scale that measures quality of life. A random sample of 20 male first semester graduate students and a random sample of 20 female first semester graduate students were taken to determine if the mean scores for quality of life differed between genders. The data are presented below.

a) If the data is assumed to be normally distributed, what is the appropriate test? Perform that test using a =. 05.

b) If the data are assumed not to be normally distributed, one appropriate nonparametric test that can be applied is the sign test. Perform this test using a =. 05.

c) Which of these tests do you believe to be the most appropriate for the data? Justify your answer.

d) What role does the central limit theorem plat in your answer to c? Explain.