Question

1. Behavioral scientists are interested in whether depressed people undergoing group therapy will perform a different number of activities of daily living after group therapy. Therefore, the scientists have randomly selected 12 depressed clients to undergo a six-week group therapy program. Use the steps of hypothesis testing to determine whether the average number of activities of daily living (shown below) obtained after therapy is significantly different from a mean number of activities of 14 that is typical for similar depressed people. Test the difference at the .05 level of significance. Indicate whether behavioral scientists should recommend group therapy for all depressed people based on evaluation of the null hypothesis at that level of significance.

Client	After Therapy
A	17
B	15
C	12
D	21
E	16
F	18
G	17
H	14
I	13
J	15
K	12
L	19

1. Using the same data and information from #1, determine whether the number of daily activities of daily living is significantly higher from the mean number of 14. Test at the .01 level of significance. Draw a conclusion from this analysis.

Step 1: Hypothesis:

Null Hypothesis:

Step 2: Same as 1.

Step 3:

One- or two-tailed test?

Cutoff score:

Step 4: t-score

Step 5: Decision, Reject null or fail to reject null at the level of significance tested

Answer 1

The hypothesis being tested is:

H0: µ = 14

Ha: µ > 14

This is a one-tailed test.

The cutoff score is 2.72.

The t-score is 2.165.

The p-value is 0.0266.

Since the p-value (0.0266) is greater than the significance level (0.01), we fail to reject the null hypothesis.

Therefore, we cannot conclude that the number of daily activities of daily living is significantly higher from the mean number of 14.

14.00000	hypothesized value
15.75000	mean Data
2.80016	std. dev.
0.80834	std. error
12	n
11	df
2.165	t
.0266	p-value (one-tailed, upper)

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