A researcher conducts an independentmeasures study examining

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

a. Does the exercise program have a significant effect? Use an alpha level of .05, two tails.
b. Compute Cohen

Solution

Control: n1=10, xbar1=12, s1^2=120.5/(10-1) =13.38889

Exercise: n2=15, xbar2=15.5, s2^2= 190/(15-1) =13.57143

a. Does the exercise program have a significant effect? Use an alpha level of .05, two tails.

Ho: mu1=mu2

Ha: mu1 not equal to mu2

The test statistic is

t=(xbar1-xbar2)/sqrt(s1^2/n1+s2^2/n2)

=(12-15.5)/sqrt(13.38889/10 + 13.57143/15)

= -2.337

Given a=0.05, the critical values are t(0.025, df=n1+n2-2=23) =-2.07 or 2.07 (from student t table)

Since t=-2.337 is less than -2.07, we reject Ho.

So we can conclude that the exercise program have a significant effect

b. Compute Cohen