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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 p-value cutoff of 0 . 1) to test the pharmaceutical companys claim that on average its new tranquilizer reduces a pa- tients pulse rate by 4.5 beats per minute. 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? 4. For a given population with = 21 . 0 cm we want to test the null hypothesis = 260 cm against the alternative hypothesis 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 = 263 . 5 cm; (c) the probability of a false negative error when = 270 cm. 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 1 = 2 for such data. Test whether the difference between these two sample means is significant using a p- value cutoff of 0.02. PRACTICE PROBLEMS 1. Book problems: 12.1-12.7; 12.11 - 12.16; 12.18- 12.22; 12.24-12.29....
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