A study reported in the Journal of Occupational and OrganizationalPsychology (De

Question

A study reported in the Journal of Occupational and OrganizationalPsychology (Dec.1992) investigated the relationship of employmentstatus to mental health. A sample of 49 unemployed men was given amental health examination using the General Health Questionnaire(GHQ). The GHQ is a widely recognized measure of present mentalhealth, with lower values indicating better mental health. The meanand standard deviation of the GHQ scores were x-bar = 10.94 and s =5.10.

a. Specify the appropriate null and alternative hypotheses if wewish to test the research hypothesis that the mean GHQ score forall unemployed men exceeds 10. Is the test one-tailed ortwo-tailed? Why?
b. If we specify = .05, what is the appropriate rejectionregion for this test?
c. Conduct the test and state your conclusion clearly in thelanguage of this exercise.

Explanation / Answer

Given n=49, xbar=10.94, s=5.1 (a) The test hypothesis is Ho:10     (alternativehypothesis) It is one-tailed test. (b) Given =0.05, Z(0.05)=1.645 (check normal table) rejection region is Z>1.645 (c) The test statistic is Z=(xbar-)/(s/n) =(10.94-10)/(5.1/sqrt(49)) =1.29 Since Z=1.29

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