A union of restaurant and foodservice workers would like to estimate this year's mean hourly wage u for foodservice workers in the U.S. Last year's mean hourly wage was $8.16, and there is good reason to believe that this year's value is greater than last year's. The union decides to do a statistical test to see if it can be concluded that the mean has increased. The union chooses a random sample of 150 wages from this year. Suppose that the population of hourly wages of foodservice workers in the U.S. has a standard deviation of $1.12 and that the union performs its hypothesis test using the 0.10 level of significance. Based on this information, answer the questions below. Carry your intermediate computations to four or more decimal places, and round your responses as indicated. (If necessary, consult a list of formulas.) (a) What are the null hypothesis Ho and the alternative hypothesis H, that the union should use for the test? Ho: O H₁: (b) Assuming that the actual value of μ is $8.33, what is the probability that the union rejects the null hypothesis? Round your response to two or more decimal places. (c) What is the probability that the union commits a Type I error? Round your response to two or more decimal places. (d) Suppose that the union decides to perform another statistical test using the same population, the same null and alternative hypotheses, and the same sample size, but for this second test the union uses a significance level of 0.01 instead of a significance level of 0.10. Assuming that the actual value of μ is $8.33, how does the probability that the union commits a Type Il error in this second test compare to the probability that the union commits a Type II error in the original test? O The probability of committing a Type II error in the second test is greater O The probability of committing a Type II error in the second test is less O The probabilities of committing a Type Il error are equal H Ix 5 0⁰ 0=0 ☐☐ X a S 0, OSO O

A union of restaurant and foodservice workers would like to estimate this year's mean hourly wage u for foodservice workers in the U.S. Last year's mean hourly wage was $8.16, and there is good reason to believe that this year's value is greater than last year's. The union decides to do a statistical test to see if it can be concluded that the mean has increased. The union chooses a random sample of 150 wages from this year. Suppose that the population of hourly wages of foodservice workers in the U.S. has a standard deviation of $1.12 and that the union performs its hypothesis test using the 0.10 level of significance. Based on this information, answer the questions below. Carry your intermediate computations to four or more decimal places, and round your responses as indicated. (If necessary, consult a list of formulas.) (a) What are the null hypothesis Ho and the alternative hypothesis H, that the union should use for the test? Ho: O H₁: (b) Assuming that the actual value of μ is $8.33, what is the probability that the union rejects the null hypothesis? Round your response to two or more decimal places. (c) What is the probability that the union commits a Type I error? Round your response to two or more decimal places. (d) Suppose that the union decides to perform another statistical test using the same population, the same null and alternative hypotheses, and the same sample size, but for this second test the union uses a significance level of 0.01 instead of a significance level of 0.10. Assuming that the actual value of μ is $8.33, how does the probability that the union commits a Type Il error in this second test compare to the probability that the union commits a Type II error in the original test? O The probability of committing a Type II error in the second test is greater O The probability of committing a Type II error in the second test is less O The probabilities of committing a Type Il error are equal H Ix 5 0⁰ 0=0 ☐☐ X a S 0, OSO O

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter8: Sequences, Series, And Probability

Section8.7: Probability

Problem 58E: What is meant by the sample space of an experiment?

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