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 u=55 with a standard deviation of 12, and the scores are normally distributed. To determine if 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. Presumably, the higher the score on the inventory is, the more depressed the patient it. 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 differently on the test? Test with the .01 level of significance for two tails. a) State the null hypothesis. Show it in symbols. b) State the alternative hypothesis. Show it in symbols. c) The critical region consists of z-scores beyond what alpha levels? d) The sample mean is equal to what? e) Within the sample, Z is equal to what? f) What conclusion is reached about the null hypothesis?

Answer 1

	Values ( X )
	59
	60
	60
	67
	65
	90
	89
	73
	74
	81
	71
	71
	83
	83
	88
	83
	84
	86
	85
	78
	79
Total	1609

To Test :-

H0 :-  

H1 :-  

Test Statistic :-

Z = 8.2559

Test Criteria :-

Reject null hypothesis if

Result :- Reject null hypothesis

Conclusion :- Accept Alternative Hypothesis

There is sufficient evidence to support the claim that patients score significantly differently on the test.