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One personality test available on the World Wide Web has a subsection designed to assess the "honesty" of the test-taker. After taking the test and seeing your score for this subsection, you're interested in the mean score u among the general population on this subsection. The website reports that µ is 140, but you believe is less than 140. To do a statistical test, you choose a random sample of 150 people and have them that take the personality test. Suppose that the population of scores on the subsection of the personality test has a standard deviation of 20 and that you perform your hypothesis test using the 0.01 level of significance. Based on this information, answer the questions below. Carry your intermediate computations to at least four decimal places, and round your responses as indicated. (If necessary, consult a list of formulas.) H. : u is What are the null and alternative hypotheses that you should use for the test? Η, : μ is What is the probability that you commit a Type I error? Round your response to at least two decimal places. Assuming that the actual value of u is 134, what is the probability that you accept the null hypothesis? Round your response to at least two decimal places. Suppose that you decide 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 you use a significance level of 0.05 instead of a significance level of 0.01. Assuming that the actual value of u is 134, how does the power of this second test compare to the power of the original test? The power of the second test is greater than the power of the original test The power of the second test is less than the power of the original test The powers of the two tests are equal

One personality test available on the World Wide Web has a subsection designed to assess the "honesty" of the test-taker. After taking the test and seeing your score for this subsection, you're interested in the mean score u among the general population on this subsection. The website reports that µ is 140, but you believe is less than 140. To do a statistical test, you choose a random sample of 150 people and have them that take the personality test. Suppose that the population of scores on the subsection of the personality test has a standard deviation of 20 and that you perform your hypothesis test using the 0.01 level of significance. Based on this information, answer the questions below. Carry your intermediate computations to at least four decimal places, and round your responses as indicated. (If necessary, consult a list of formulas.) H. : u is What are the null and alternative hypotheses that you should use for the test? Η, : μ is What is the probability that you commit a Type I error? Round your response to at least two decimal places. Assuming that the actual value of u is 134, what is the probability that you accept the null hypothesis? Round your response to at least two decimal places. Suppose that you decide 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 you use a significance level of 0.05 instead of a significance level of 0.01. Assuming that the actual value of u is 134, how does the power of this second test compare to the power of the original test? The power of the second test is greater than the power of the original test The power of the second test is less than the power of the original test The powers of the two tests are equal

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 30PPS
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One personality test available on the World Wide Web has a subsection designed to assess the "honesty" of the test-taker. After taking the test and seeing your score for this subsection, you're interested in the mean score u among the general population on this subsection. The website reports that µ is 140, but you believe is less than 140. To do a statistical test, you choose a random sample of 150 people and have them that take the personality test. Suppose that the population of scores on the subsection of the personality test has a standard deviation of 20 and that you perform your hypothesis test using the 0.01 level of significance. Based on this information, answer the questions below. Carry your intermediate computations to at least four decimal places, and round your responses as indicated. (If necessary, consult a list of formulas.) H. : u is What are the null and alternative hypotheses that you should use for the test? Η, : μ is What is the probability that you commit a Type I error? Round your response to at least two decimal places. Assuming that the actual value of u is 134, what is the probability that you accept the null hypothesis? Round your response to at least two decimal places. Suppose that you decide 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 you use a significance level of 0.05 instead of a significance level of 0.01. Assuming that the actual value of u is 134, how does the power of this second test compare to the power of the original test? The power of the second test is greater than the power of the original test The power of the second test is less than the power of the original test The powers of the two tests are equal
Transcribed Image Text:One personality test available on the World Wide Web has a subsection designed to assess the "honesty" of the test-taker. After taking the test and seeing your score for this subsection, you're interested in the mean score u among the general population on this subsection. The website reports that µ is 140, but you believe is less than 140. To do a statistical test, you choose a random sample of 150 people and have them that take the personality test. Suppose that the population of scores on the subsection of the personality test has a standard deviation of 20 and that you perform your hypothesis test using the 0.01 level of significance. Based on this information, answer the questions below. Carry your intermediate computations to at least four decimal places, and round your responses as indicated. (If necessary, consult a list of formulas.) H. : u is What are the null and alternative hypotheses that you should use for the test? Η, : μ is What is the probability that you commit a Type I error? Round your response to at least two decimal places. Assuming that the actual value of u is 134, what is the probability that you accept the null hypothesis? Round your response to at least two decimal places. Suppose that you decide 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 you use a significance level of 0.05 instead of a significance level of 0.01. Assuming that the actual value of u is 134, how does the power of this second test compare to the power of the original test? The power of the second test is greater than the power of the original test The power of the second test is less than the power of the original test The powers of the two tests are equal
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