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The article "Uncertainty Estimation in Railway Track Life-Cycle Cost"t presented the following data on time to repair (min) a rail break in the high rail on a curved track of a certain railway line. 159 120 480 149 270 547 340 43 228 202 240 218 IA USE SALT A normal probability plot of the data shows a reasonably linear pattern, so it is plausible that the population distribution of repair time is at least approximately normal. The sample mean and standard deviation are 249.7 and 145.1, respectively. (a) Is there compelling evidence for concluding that true average repair time exceeds 200 min? Carry out a test of hypotheses using a significance level of 0.05. State the appropriate hypotheses. • Hoi H- 200 H:H > 200 O Hoi H< 200 H:- 200 O Hoi - 200 H: 200 O Ho: H- 200 H:H< 200 O Ho: H > 200 H:- 200 Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) P-value - What can you conclude? O There is compelling evidence that the true average repair time exceeds 200 min. O There is not compelling evidence that the true average repair time exceeds 200 min. (b) Using a- 150, what is the type II error probability of the test used in (a) when true average repair time is actually 300 min? That is, what is B(300)? (Round your answer to two decimal places. You will need to use the appropriate table in the Appendix of Tables to answer this question.) B(300) -

The article "Uncertainty Estimation in Railway Track Life-Cycle Cost"t presented the following data on time to repair (min) a rail break in the high rail on a curved track of a certain railway line. 159 120 480 149 270 547 340 43 228 202 240 218 IA USE SALT A normal probability plot of the data shows a reasonably linear pattern, so it is plausible that the population distribution of repair time is at least approximately normal. The sample mean and standard deviation are 249.7 and 145.1, respectively. (a) Is there compelling evidence for concluding that true average repair time exceeds 200 min? Carry out a test of hypotheses using a significance level of 0.05. State the appropriate hypotheses. • Hoi H- 200 H:H > 200 O Hoi H< 200 H:- 200 O Hoi - 200 H: 200 O Ho: H- 200 H:H< 200 O Ho: H > 200 H:- 200 Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) P-value - What can you conclude? O There is compelling evidence that the true average repair time exceeds 200 min. O There is not compelling evidence that the true average repair time exceeds 200 min. (b) Using a- 150, what is the type II error probability of the test used in (a) when true average repair time is actually 300 min? That is, what is B(300)? (Round your answer to two decimal places. You will need to use the appropriate table in the Appendix of Tables to answer this question.) B(300) -

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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The article "Uncertainty Estimation in Railway Track Life-Cycle Cost" presented the following data on time to repair (minutes) a rail break in the high rail on a curved track of a certain railway line: 159, 120, 480, 149, 270, 547, 340, 43, 228, 202, 240, 218 A normal probability plot of the data shows a reasonably linear pattern, suggesting that the population distribution of repair time is approximately normal. The sample mean and standard deviation are 249.7 and 145.1, respectively. (a) Is there compelling evidence for concluding that true average repair time exceeds 200 minutes? Perform a hypothesis test using a significance level of 0.05. State the appropriate hypotheses. Hypotheses: - \( H_0: \mu = 200 \) - \( H_a: \mu > 200 \) Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) \( t = \) P-value = Conclusion: - There is compelling evidence that the true average repair time exceeds 200 minutes. - There is not compelling evidence that the true average repair time exceeds 200 minutes. (b) Using \( \alpha = 150 \), what is the type II error probability of the test used in (a) when the true average repair time is actually 300 minutes? In other words, what is \( \beta (300) \)? (Round your answer to two decimal places. You will need to use the appropriate table in the Appendix of Tables to answer this question.) \( \beta (300) = \)
Transcribed Image Text:The article "Uncertainty Estimation in Railway Track Life-Cycle Cost" presented the following data on time to repair (minutes) a rail break in the high rail on a curved track of a certain railway line: 159, 120, 480, 149, 270, 547, 340, 43, 228, 202, 240, 218 A normal probability plot of the data shows a reasonably linear pattern, suggesting that the population distribution of repair time is approximately normal. The sample mean and standard deviation are 249.7 and 145.1, respectively. (a) Is there compelling evidence for concluding that true average repair time exceeds 200 minutes? Perform a hypothesis test using a significance level of 0.05. State the appropriate hypotheses. Hypotheses: - \( H_0: \mu = 200 \) - \( H_a: \mu > 200 \) Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) \( t = \) P-value = Conclusion: - There is compelling evidence that the true average repair time exceeds 200 minutes. - There is not compelling evidence that the true average repair time exceeds 200 minutes. (b) Using \( \alpha = 150 \), what is the type II error probability of the test used in (a) when the true average repair time is actually 300 minutes? In other words, what is \( \beta (300) \)? (Round your answer to two decimal places. You will need to use the appropriate table in the Appendix of Tables to answer this question.) \( \beta (300) = \)
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