Question

A psychologist develops a new inventory to measure depression. Using a very large standardization group of "normal" individuals, the mean score on this test is µ = 55 with σ = 12, and the scores are normally distributed. To determine whether the test is sensitive in detecting those individuals that are severely depressed, a random sample of patients who are described as depressed by a therapist is selected and given the test. The higher the score on the inventory, the more depressed the patient is. The data are as follows: 59, 60, 60, 67, 65, 90, 89, 73, 74, 81, 71, 71, 83, 83, 88, 83, 84, 86, 85, 78, 79. Do patients score significantly different than the “normal” individuals on the test? Test with the .01 level of significance. Draw the comparison distribution and locate the sample mean and its associated z-score on the comparison distribution.

Answer 1

The Null Hypothesis: H0: = 55. The mean score of patients in the depression test is equal to 55.

The Alternative Hypothesis: 55 : The mean score of patients in the depression test is different from 55.

The critical regions are Z > 2.576 and Z < -2.576

The mean = Sum Of observations / 21 = 1609 / 21 = 76.62

The Z value

Since Z observed is > 2.576, we reject H0.

There is sufficient evidence at the 0.01 level to conclude that the mean score of patients in the depression test is different from 55.