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Unformatted text preview: 1 Exercises for Chapter 8 1. a) When a null hypothesis is rejected, there is risk of committing which type of error? b) When a null hypothesis is not rejected, there is risk of committing which type of error? 2. In 10-mph crash tests, 25% of a certain type of automobiles sustain no visible damage. A modified bumper design has been proposed in an effort to increase this percentage. Let p denote the proportion of all cars with this new bumper that sustain no visible damage in 10-mph crash tests. The hypotheses to be tested are H : p = 0 . 25 vs H : p &gt; . 25. The test will based on an experiment involving n = 20 independent crashes of car prototypes with the new bumper design. Let X denote the number of crashes resulting in no visible damage, and consider the test procedure that rejects the null hypothesis if X 8. a) Use the binomial table to find the probability of type I error. b) Use the binomial table to find (0 . 3), i.e. the probability of type II error when the true value of p is 0 . 3. 3. Consider the car crash experiment of Exercise 2, where H : p = 0 . 25 is tested against H : p &gt; . 25, but suppose that n = 50 cars are crashed, and the null hypothesis is rejected if the number of crashes, X , resulting in no visible damage is X 15. a) Use the normal approximation to the binomial probabilities to find the probability of type I error. b) Use the normal approximation to the binomial probabilities to find the probability of type II error when the true value of p is 0 . 3. 4. An appliance manufacturer is considering the purchase of a new machine for cutting sheet metal parts. If is the average number of metal parts cut per hour by her old machine and is the corresponding average for the new machine, the manufacturer wants to test the null hypothesis H : = against a suitable alternative. What should the alternative be if (a) she does not want to buy the new machine unless there is evidence it is more productive than the old one; (b) she wants to buy the new machine (which has some other nice features) unless there is evidence it is less productive than the old one?evidence it is less productive than the old one?...
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This note was uploaded on 01/11/2012 for the course STAT 401 taught by Professor Akritas during the Fall '00 term at Penn State.
- Fall '00