lecture16

# lecture16 - Test of a hypothesis A sewer pipe manufacturer...

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Test of a hypothesis I A sewer pipe manufacturer claim that, on average their pipes have breaking strength beyond 2,400 pounds. Suppose you have a dataset consisting 50 measurements, namely the breaking strength measured on 50 sections of a sewer pipe the company produced. Can you test the claim in a ‘convincing’ way? I Null hypothesis: H 0 : μ 2 , 400, where μ is the mean breaking strength of the sewer pipe the company can produce. I Alternative hypothesis: H a : μ > 2 , 400. I Does the data show convincing evidence to reject H 0 in favor of H a . I From the actual data y , ¯ y = 2 , 460 pounds per linear foot, and s = 200 pounds per linear foot.

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I For the z-value of that particular dataset, if we are comparing it with the value 1.645, and decide to reject H 0 whenever the sample z -value exceeding 1.645. This is called a level- α test, and the α is given by .05. Another interpretation for this value is the type I error probability. Why? remember we are using the rejection region (1 . 645 , + ); if the null is indeed true, we may still have α probability of seeing z -values in that region. Since we have decided that’s the rejection region, then can you ﬁgure out the implication? I
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lecture16 - Test of a hypothesis A sewer pipe manufacturer...

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