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Lab8withSol - Statistics 103 Lab 8 LAB PROBLEMS 1 A new...

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Statistics 103: Lab 8 LAB PROBLEMS 1. A new tranquilizer given to n = 16 patients re- duced their pulse rate on the average by 4 . 36 beats per minute with a standard deviation of 0 . 36 beats per minute. Assuming that such data can be look upon as a random sample from a normal popula- tion, use a hypothesis test (with a p-value cutoff of 0 . 1) to test the pharmaceutical companys claim that on average it’s new tranquilizer reduces a pa- tients pulse rate by 4.5 beats per minute. answer: Reject the company’s claim (p-value 0.0703) 2. Read the comic http://xkcd.com/882/ then do the following problem: 3. Some scientists are exploring a possible link be- tween acne and consuming various colors of jelly beans. They choose 20 colors of jelly beans and conduct hypothesis tests for each color with a p- value cutoff of 0.05 in each test. They find no link between 19 of the colors of jelly beans and acne, getting p-values higher than 0.05. However, they found that there was a significant link between green jelly beans and acne, with a p-value of less than 0.05. They rush to publish their findings, but their article is rejected by every journal they submit to. Why? answer: The scientists are performing multiple hy- pothesis tests with p-value cutoff at 0.05, so the probability that they get a false positive when there is truly no link in each test is 0.05. If they perform 20 of these tests, then there is a good chance that one of them will return a false positive. 4. For a given population with σ = 21 . 0 cm we want to test the null hypothesis μ = 260 cm against the alternative hypothesis μ 6 = 260 cm on the basis of a random sample of size n = 36. If the null hypothesis is rejected when X is less than 253 cm or great than 267 cm and otherwise it is accepted, find (a) the probability of a false positive error; (b) the probability of a false negative error when μ = 263 . 5 cm; (c) the probability of a false negative error when μ = 270 cm. answer: (a) about 0.05 (b) 0.84 (c) 0.196 5. An investigation of two kinds of photocopiers showed that a random sample of 60 failures of one kind of photocopier took on the average 84.2 min- utes to repair, while a random sample of 60 failures of another kind of photocopier took on average 91.6 minute to repair (where the sample standard de- viations for the two samples were 19 . 4 and 18 . 8, respectively). Suppose, on the basis of collateral information, it can be assumed that σ 1 = σ 2 for such data. Test whether the difference between these two sample means is significant using a p- value cutoff of 0.02.
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