You have an internship at the Gillette World Shaving Headquarters in Boston. The company is devel-...

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You have an internship at the Gillette World Shaving Headquarters in Boston. The company is devel- oping a new line of razors and management asks you to conduct market research on men's shaving habits. You conduct a survey where a sample of men report the number of times that they shave in one week. Suppose you know that the number of times per week men shave in the population is normally distributed with a variance of 2. You hypothesize that in the population, men shave 4 times per week. You pick 10 persons at random and you find that they shave 3 times per week on average. a. (5 pts) Is this a one-sided or two-sided hypothesis test? Why? b. (5 pts) Complete a hypothesis test at a 5 percent significance level. Clearly specify the following: i. The null and alternative hypotheses. ii. The critical values for the test. iii. Any values that will cause you to reject your null hypothesis. iv. Your actual test statistic. v. The conclusion you draw from your results. Now, suppose that you randomly select 121 men and find they shave 3.98 times per week on average. c. (5 pts) Complete a hypothesis test at a 10 percent significance level. Report all of the same items requested in part b. for this hypothesis test. d. (5 pts) What is the p-value in this case? e. (5 pts) Calculate the power of this test if the true mean is 3.8 times per week. You have an internship at the Gillette World Shaving Headquarters in Boston. The company is devel- oping a new line of razors and management asks you to conduct market research on men's shaving habits. You conduct a survey where a sample of men report the number of times that they shave in one week. Suppose you know that the number of times per week men shave in the population is normally distributed with a variance of 2. You hypothesize that in the population, men shave 4 times per week. You pick 10 persons at random and you find that they shave 3 times per week on average. a. (5 pts) Is this a one-sided or two-sided hypothesis test? Why? b. (5 pts) Complete a hypothesis test at a 5 percent significance level. Clearly specify the following: i. The null and alternative hypotheses. ii. The critical values for the test. iii. Any values that will cause you to reject your null hypothesis. iv. Your actual test statistic. v. The conclusion you draw from your results. Now, suppose that you randomly select 121 men and find they shave 3.98 times per week on average. c. (5 pts) Complete a hypothesis test at a 10 percent significance level. Report all of the same items requested in part b. for this hypothesis test. d. (5 pts) What is the p-value in this case? e. (5 pts) Calculate the power of this test if the true mean is 3.8 times per week.