Question

A researcher conducts a 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 the program was completed, 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

Required:
a. Does the exercise program have a significant effect? Use an alpha level of .05, two tails.
b. Compute Cohen's d to measure the size of the treatment effect.
c. Calculate the two-sample t-test. To receive fiull credit, please clearly label your pooled variance, estimated standard error, and final t-score.
d. What t values form the boundary for the critical region?

Answer 1

Check the explanation

Explanation:

Hypotheses are:

`H_(0):\mu_(1)=\mu_(2),H_(1):\mu_(1)\\eq \mu_(2)`

Following is the output of t test:

Hypothesis Test: Independent Groups (t-test, pooled variance)

X1 X2

12 15.5 mean

3.6591 3.6839 std. dev.

10 15 n

23 df

-3.5000 difference (X1 - X2)

13.4999 pooled variance

3.6742 pooled std. dev.

1.5000 standard error of difference

0 hypothesized difference

-2.33 t

.0287 p-value (two-tailed)

The p-value is:

p-value = 0.0287

Since p-value is less than 0.05 so we reject the null hypothesis. That is we can conclude that the exercise program have a significant effect.

(b)

The cohen's d is

`d=\left |\frac{\bar{x}_(1)-\bar{x}_(2)}{s_(p)} \right |=\left |(12-15.5)/(3.6742 ) \right |=0.95`