A new treatment for depression is under investigation. Patients are given a psyc

Question

A new treatment for depression is under investigation. Patients are given a psychological test before and after treatment in order to determine the effectiveness of the treatment. Researchers hope to find a difference in test scores before and after treatment. A 95% confidence interval for the population average difference in evaluation scores (before-after) is given by (0.25, 3.75), which was computed based on a random sample of 36 patients.

f Is there a significant difference in test scores (before- after) on average? Perform an appropriate hypothesis test at the 10% level. Step 1: Define parameter of interest and state the hypothesis. Parameter: HO: lla Significance level ?- Step 2: Verify necessary data conditions and compute an appropriate test statistie: Step 3: Assuming the HO is true, construct rejection region: Step 4: Decide whether the result is statistically significant (reject or fail to reject HO): Step 5: Report the conclusion in the context of the problem (question of interest). gCompute the power of the test assuming that the true difference is 2

Explanation / Answer

Solution:

Step 1:

Parameter: Ho = µd = 0, Ha: µd ? 0 and Significance level, a = 0.05

Step 2:

Test Statistics

t = (X-bard - µd)/(sd/?n)

t = (2 - 0)/ (0.862/?36)

t = 13.92

Step 3:

Degrees of freedom, df = n - 1 = 36-1 = 35

Using t-tables, the critical value is

t (0.05/2, 35) = 2.030

Rejection region - If test statistics is greater than 2.030 or less than -2.030, we reject Ho.

Step 4:

Since test statistics is greater than the critical value, we reject Ho.

Step 5:

Hence, there is difference in test scores before and after treatment.

f. Using t-tables, the critical value at a = 0.10 is

t (0.10/2, 35) = 1.690

Since test statistics is greater than the critical value, we reject Ho.

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