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?

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temmydbrain temmydbrain · Answer 1 · 2020-05-14T04:43:16+02:00

Answer:

Check the explanation

Step-by-step explanation:

Hypotheses are:

[tex]H_{0}:\mu_{1}=\mu_{2},H_{1}:\mu_{1}\neq \mu_{2}[/tex]

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

[tex]d=\left |\frac{\bar{x}_{1}-\bar{x}_{2}}{s_{p}} \right |=\left |\frac{12-15.5}{3.6742 } \right |=0.95[/tex]