w13_HTalpha_post (1)

w13_HTalpha_post (1) - mileage than the old engine at = 5%...

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(PS5 Q11) In the past, the gas mileage of a compact car has a normal distribution with mean μ=30 miles per gallon and standard deviation of four miles per gallon. Engineers redesigned the engine of this car and tested the gas mileage of a simple random sample of 100 new cars. They want to prove that the new cars have higher mean gas mileage. Assume that the standard deviation for the new cars remains at four miles per gallon. a. If the manufacturer always rejects the null hypothesis, H0 : μ = 30, when the sample mean mileage is greater than 30.7. What is the significance level, , of the test? b. If a sample mean of x = 30.8 has been observed, what is the p-value? c. If we change the sample size to n = 25 and everything else remains the same, do you need to use t distribution when determining the critical value of the test or when constructing confidence intervals? Explain briefly. d. How large should the sample mean mileage of the 100 new cars be so that the automobile manufacturer can conclude that the new engine yields a higher mean gas
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Unformatted text preview: mileage than the old engine at = 5% level? (Final 2003, Q2) A battery manufacturer claims that his company produces batteries with a mean life of 130 hours. An investigator working for an independent consumer protection agency wishes to test the credibility of the manufacturer’s claim. She randomly selects 100 batteries produced by the process and decides that she will believe the manufacturer’s claim only if the sample mean is not less than 129 hours. It is known that the standard deviation of the manufacturing process is 5 hours. (a) What is null hypothesis, alternative hypothesis? (b) What is the rejection region? (c) What is the level of significance of the test (α)? (d) If the investigator wishes to control the Type I error of the test to be 1%, what will be her rejection region? (e) If the sample mean of the 100 batteries that the investigator selected is 128 hours, what decision should she make at 1% level of significance?...
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w13_HTalpha_post (1) - mileage than the old engine at = 5%...

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