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1) For each of the following scenarios, define the null hypothesis (Ho) and the alternate hypothesis (H1): (a) The mean diameter of bolts produced by Machine 2 is tested to see if is different from the diameter of bolts produced by Machine 1 (b) The standard deviation of bolts produced by Machine 1 is tested to see if it is greater than the standard deviation of bolts produced by Machine 2. (c) The proportion of bolts produced by Machine 2 that do not meet specification is 2% less than that of bolts produced by Machine 1. Note: For #1, in addition to listing the hypotheses on the cover sheet, include a short explanation of the reason(s) for choosing those hypotheses as part of your supplementary materials.

1) For each of the following scenarios, define the null hypothesis (Ho) and the alternate hypothesis (H1): (a) The mean diameter of bolts produced by Machine 2 is tested to see if is different from the diameter of bolts produced by Machine 1 (b) The standard deviation of bolts produced by Machine 1 is tested to see if it is greater than the standard deviation of bolts produced by Machine 2. (c) The proportion of bolts produced by Machine 2 that do not meet specification is 2% less than that of bolts produced by Machine 1. Note: For #1, in addition to listing the hypotheses on the cover sheet, include a short explanation of the reason(s) for choosing those hypotheses as part of your supplementary materials.

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 31PPS
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1) For each of the following scenarios, define the null hypothesis (Ho) and the alternate hypothesis (H1): (a) The mean diameter of bolts produced by Machine 2 is tested to see if is different from the diameter of bolts produced by Machine 1 (b) The standard deviation of bolts produced by Machine 1 is tested to see if it is greater than the standard deviation of bolts produced by Machine 2. (c) The proportion of bolts produced by Machine 2 that do not meet specification is 2% less than that of bolts produced by Machine 1. Note: For #1, in addition to listing the hypotheses on the cover sheet, include a short explanation of the reason(s) for choosing those hypotheses as part of your supplementary materials.
Transcribed Image Text:1) For each of the following scenarios, define the null hypothesis (Ho) and the alternate hypothesis (H1): (a) The mean diameter of bolts produced by Machine 2 is tested to see if is different from the diameter of bolts produced by Machine 1 (b) The standard deviation of bolts produced by Machine 1 is tested to see if it is greater than the standard deviation of bolts produced by Machine 2. (c) The proportion of bolts produced by Machine 2 that do not meet specification is 2% less than that of bolts produced by Machine 1. Note: For #1, in addition to listing the hypotheses on the cover sheet, include a short explanation of the reason(s) for choosing those hypotheses as part of your supplementary materials.
4) Your construction company has purchased two lots of southern yellow pine lumber, both supposedly with 4% moisture content. The mean perpendicular compression strength of the first lot is tested with a sample of n1 = 13 boards, yielding x = 14.8 MPa. A test of a sample of n2 = 13 boards from the second lot, which arrives after several days of rain and is wet, results in x, = 13.7 MPa. The population standard deviations are known to be the same, at of = ož = o? = 0.5 MPa. Complete the following: (a) Conduct a hypothesis test with a = 0.01 to see if the mean perpendicular compression strengths of the two populations are the same or not. Your work should show all 7 steps of the hypothesis testing procedure. On the cover sheet, just write your conclusion. (i.e., "There is/is not sufficient evidence at the a = 0.01 level of significance to conclude that the mean perpendicular compression strengths..") (b) For the results of your hypothesis test in part (a), what is the p-value for this test? (c) What is the probability that you will incorrectly reject the null hypothesis? Provide the correct symbol and value in your answer on the answer sheet. (d) To calculate the probability that you will fail to reject an incorrect null hypothesis, suppose that the true difference in mean perpendicular compression strength between the two lots is A= µ1 – µz = 0.5 MPa. Calculate this probability, and provide the correct symbol and value in your answer on the answer sheet. (e) Suppose that you want the reduce the probability of a Type II error to ß =0.10, so that = 0-1(0.10) = 1.28. If all other parts of the problem remain the same, what is the minimum number of samples that you will need? (f) Suppose you measure the sample standard deviations and find that s, = 0.51 MPa and S2 = 0.75 MPa, with sample sizes the same at 13 boards each. Conduct a hypothesis test with a = 0.05 to see if the standard deviations of the two lots are the same or not. As in (a), show all 7 steps and write the full conclusion on your answer sheet.
Transcribed Image Text:4) Your construction company has purchased two lots of southern yellow pine lumber, both supposedly with 4% moisture content. The mean perpendicular compression strength of the first lot is tested with a sample of n1 = 13 boards, yielding x = 14.8 MPa. A test of a sample of n2 = 13 boards from the second lot, which arrives after several days of rain and is wet, results in x, = 13.7 MPa. The population standard deviations are known to be the same, at of = ož = o? = 0.5 MPa. Complete the following: (a) Conduct a hypothesis test with a = 0.01 to see if the mean perpendicular compression strengths of the two populations are the same or not. Your work should show all 7 steps of the hypothesis testing procedure. On the cover sheet, just write your conclusion. (i.e., "There is/is not sufficient evidence at the a = 0.01 level of significance to conclude that the mean perpendicular compression strengths..") (b) For the results of your hypothesis test in part (a), what is the p-value for this test? (c) What is the probability that you will incorrectly reject the null hypothesis? Provide the correct symbol and value in your answer on the answer sheet. (d) To calculate the probability that you will fail to reject an incorrect null hypothesis, suppose that the true difference in mean perpendicular compression strength between the two lots is A= µ1 – µz = 0.5 MPa. Calculate this probability, and provide the correct symbol and value in your answer on the answer sheet. (e) Suppose that you want the reduce the probability of a Type II error to ß =0.10, so that = 0-1(0.10) = 1.28. If all other parts of the problem remain the same, what is the minimum number of samples that you will need? (f) Suppose you measure the sample standard deviations and find that s, = 0.51 MPa and S2 = 0.75 MPa, with sample sizes the same at 13 boards each. Conduct a hypothesis test with a = 0.05 to see if the standard deviations of the two lots are the same or not. As in (a), show all 7 steps and write the full conclusion on your answer sheet.
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