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Unformatted text preview: 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 pvalue 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 (pvalue 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 pvalues higher than 0.05. However, they found that there was a significant link between green jelly beans and acne, with a pvalue 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 pvalue 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. answer: The difference between these two sam ple means is not statistically significant (pvalue 0.034) PRACTICE PROBLEMS 1. Book problems: 12.112.7; 12.11  12.16; 12.18 12.22; 12.2412.29....
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This note was uploaded on 09/13/2011 for the course STA 103 taught by Professor Drake during the Spring '09 term at UC Davis.
 Spring '09
 Drake
 Statistics, Standard Deviation

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