AMS 310 Second Practice Test 3

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Statistics

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Jan 9, 2024

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AMS 310 Second Practice Test 3 Fred Rispoli Based on Chapters 7, 8 and 9 1. A printer company claims that the mean warm-up time of a certain brand of printers is at most 15 seconds. An engineer from another company is conducting a statistical test to show that this is an underestimate. a) State the testing hypotheses. b) The test yielded a p-value of 0.035. What would be the decision of the test if  = 0.05? c) The test yielded a p-value of 0.035. What would be the decision of the test if  = 0.01? d) Suppose that a further study established that the true mean warm-up time is 14 seconds. If the engineer made the decision to reject H 0 , did the engineer make the correct decision? If not, what types of error was made? e) Suppose that a further study established that the true mean warm-up time is 16 seconds. If the engineer made the decision to reject H 0 , did the engineer make the correct decision? If not, what types of error was made? 2. The lifetime of certain type of car engine is normally distributes with a mean of 200,000 miles and a standard deviation of 30,000 miles. An automaker claims that the new year model has an engine with a longer average lifetime. A sample of 16 cars with this type of engine from the new model is obtained for a test. Consider a rejection region { X ≥ 215,000}. a) What hypotheses should be tested? b) Find the probability of a Type 1 error. c) Suppose that a further study establishes that, in fact, the average lifetime of the new engine is 210,000 miles. Find the probability of a type II error. 3. A group of 36 male bowlers claimed that their average score is at least 190. A sample of their scores indicated that their average score was 186, with a known standard deviation of the population equal to 6, and the scores are normally distributed. Test the claim at the  = 0.05 level. Show all work involved (i.e., the five steps for hypothesis testing).

4. A sample of 25 speed guns is obtained for checking accuracy in the range between 50 and 60 mph. The sample average of the errors is 1.3 mph, and the sample standard deviation is 1.5 mph. a) Construct a 99% confidence interval for the population mean error. b) Based on the confidence interval obtained in part a), is there enough evidence to conclude that the error is significantly different from zero? Explain your answer. 5. A manufacturer claims that the standard deviation of the drying time of a certain type of paint is 20 minutes. A sample of ten test panels produced a standard deviation of 22 minutes. Test the claim at  = 0.10. Use the 5-step method. You do not need to give a p-value. 6. The shelf life (duration until expiration date in months) of a certain ointment is known to have a normal distribution. A sample of size 120 tubes of ointment gives a sample mean of 36.1 months and a standard deviation of 3.7. a) Construct a 95% confidence interval of the population mean shelf life. b) Suppose a researcher believed before the experiment that  = 4. What would be the required sample size to estimate the population mean to be within 0.5 months with 99% confidence? 7. In animal cancer research the potential of human drugs and other substances are studied. Four hundred ppm of benzidine dihydrochloride is given to each of the male and female mice from a certain strain. In one of these experiments, tumors were found in 54 out of 484 male mice and 127 out of 429 female mice. a) Find a 99% confidence interval for the difference between the tumor rate of male mice and female mice. b) Test if the tumor rate of female mice is higher than the tumor rate of male mice. Use  = 0.01 to test the claim.

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