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Unformatted text preview: STATW1211.005 Prof. Zhang TR 02:40P-03:55P Homework 7 Solutions Textbook: Probability and statistics for engineering and the sciences (7 th edition) by Jay L. Devore Chapter 8: Question 9 a. R 1 is most appropriate, because x either too large or too small contradicts p = .5 and supports p .5. b. A type I error consists of judging one of the two companies favored over the other when in fact there is a 50-50 split in the population. A type II error involves judging the split to be 50-50 when it is not. c. X has a binomial distribution with n = 25 and p = 0.5. P(type I error) = when X ~ Bin(25, .5)) = B(7; 25,.5) + 1 B(17; 25,.5) = .044 d. when p = .4) = B(17; 25,.5) B(7, 25,.4) = 0.845, and also. e. x = 6 is in the rejection region R 1 , so H is rejected in favor of H a . Question 13 a. , where Z is a standard normal r.v. b. P(rejecting H when when . Similarly, when . In general, we have P(type I error) < .01 when this probability is calculated for a value of less than 100. The boundary value...
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