A researcher conducts an independent-measures study examining the effectiveness

Question

A researcher conducts an independent-measures study examining the effectiveness of a group exercise program at an assisted living facility for elderly adults. One group of residents is selected to participate in the program, and a second group serves as a control. After 6 weeks, the researcher records a combined score measuring balance and strength for each individual. The data are as follows: Control Exercise n = 10 n = 15 M = 12 M = 15.5 SS = 120.5 SS = 190.0 Use an alpha of .05, two-tailed. Write a results section including the following information: - Mean and standard deviation for each sample - Whether or not there was a significant difference between the groups (i.e. does the exercise program have a significant effect?) - What does this indicate? (Note, do not discuss the results here, just state what the test results indicate) - Cohen’s d, and an interpretation of obtained d

Explanation / Answer

H0: 1 - 2 = 0 i.e. (1 = 2) (No difference)

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

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)

         = (10-1)*3.66^2+(15-1)*3.68^2/9+14

         = 120.5+190/23

         = 13.5

tSTAT=(X1-X2)-(µ1-µ2)/Sp^2(1/n1+1/n2)

       =(12-15.5)-0/13.5(1/10+1/15)

       =-3.5/1.5

       =-2.33

tCRIT is +/-2.068 and hence reject the null hypothesis since tSTAT < tCRIT

SDpooled=S1^2+S2^2/2

             =13.39+13.57/2

             =3.67

Cohen's d = (M2 - M1) SDpooled

                 = 15.5-12/3.67

                 = 0.95

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