Make sure to show all the steps in your analyses. Clearly label each question an

Question

Make sure to show all the steps in your analyses. Clearly label each question and your answer. When submitting your work, put your papers in order and staple them. Downs & Abwender (2002) evaluated soccer players and swimmers to determine whether routine blows to the head experienced by soccer players produced long-term neurological deficits. Neurological tests were administered to mature soccer players and swimmers, see the following data:

Swimmers: 10, 8, 7, 9, 13, 7

Soccer Players: 7, 4, 9, 3, 7, 6

a. Perform the appropriate test by hand and evaluate if neurological test scores were significantly different between the soccer players and the swimmers.

Explanation / Answer

a)      H0: 1 - 2 = 0 i.e. (1 = 2)

H1: 1 - 2 0 i.e. (1 2)

            

Assuming population variances are equal, we would have to calculate pooled-variance t-Test

Sp^2= (n1-1)S1^2+(n2-1)S2^2/(n1-1)+(n2-1)

         = (6-1)*2.28^2+(6-1)*2.19^2/5+5

         = 25.992+23.9805/10

         =4.99725

tSTAT=(X1-X2)-(µ1-µ2)/Sp^2(1/n1+1/n2)

       =(9-6)-0/4.99725(1/6+1/6)

      =2.3255

tCRIT is 2.2282 and hence reject the null hypothesis as tSTAT lies in the rejection region.

Swimmers Soccer Players 10 7 8 4 7 9 9 3 13 7 7 6 9 6 Mean 2.2803509 2.19089023 Std_Dev

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