# Statistics - Elements of a Test Hypothesis

**Topics:**Statistical hypothesis testing, Null hypothesis, Statistics

**Pages:**5 (1699 words)

**Published:**March 25, 2013

Example. A study reported in the Journal of Occupational and Organizational Psychology investigated the relationship of employment status to mental health. Each of a sample of 49 unemployed men was given a mental health examination using the General Health Questionnaire (GHQ). The GHQ is widely recognized measure of present mental health , with lower values indicating better mental health. The mean and standard deviation of the GHQ scores were x = 10.94 and s = 5.10, ¯ respectively. (a). Specify the appropriate null and alternative hypothesis if we wish to test the research hypothesis that the mean GHQ score for all unemployed men exceeds 10. Is the test one-tailed or two-tailed? (b). If we specify α = 0.05, what is the appropriate rejection region for this test? (c). Conduct the test, and state your conclusion clearly in the language of this exercise. Find the p-value of the test. (Ans. H0 : µ = 10; Ha : µ > 10; One-tailed test; Rejection region: Z > 1.645; Test score: Z = 1.29; Do not reject H0 , GHQ score does not exceeds 10; p-value = 0.0985) Example. A consumer protection group is concerned that a ketchup manufacturer is ﬁlling its 20-ounce family-size containers with less than 20 ounces of ketchup. The group purchases 49 family-size bottles of this ketchup, weigh the contents of each, and ﬁnds that the mean weight is 19.86 ounces, and the standard deviation is equal to 0.22 ounces. (a). Do the data provide suﬃcient evidence for the consumer group to conclude that the mean ﬁll per family-size bottle is les than 20 ounces? Test using α = 0.05. (b). Find the p-value of the your test in part (a). (Ans. H0 : = 20; Ha : < 20; Rejection Region is Z < −1.645 (one-tailed test); test score Z = −4.45; Reject H0 at α = 0.05, suﬃcient evidence to say that the mean ﬁll per family-size bottle is less than 20 ounces; p-value = 0) Example. State University uses thousands of ﬂuorescent light bulbs each year. The brand of bulb it currently uses has a mean life of 900 hours. A manufacturer claims that its new brands of bulbs, which cost the same as the brand the university currently uses, has a mean life of more than 900 hours. The university has decided to purchase the new brand if, when tested, the test evidence supports the manufacturer’s claim at the .10 signiﬁcance level. Suppose 99 bulbs were tested with...

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