The article "Uncertainty Estimation in Railway Track Life-Cycle Cost"+ 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 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. Ο Η: μ = 200 Haμ > 200 O Ho: μ = 200 Ha: <200 O Ho: M = 200 Haμ 200 Ο Ηρ: μ > 200 Ha μ = 200 O Ho: μ<200 Ha: μ = 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 = 0.18 P-value = 0.8601 What can you conclude? Х × ○ There is compelling evidence that the true average repair time exceeds 200 min. ● There is not compelling evidence that the true average repair time exceeds 200 min. (b) Using 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 ẞ(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.) ẞ(300) = 0.85 ×
The article "Uncertainty Estimation in Railway Track Life-Cycle Cost"+ 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 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. Ο Η: μ = 200 Haμ > 200 O Ho: μ = 200 Ha: <200 O Ho: M = 200 Haμ 200 Ο Ηρ: μ > 200 Ha μ = 200 O Ho: μ<200 Ha: μ = 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 = 0.18 P-value = 0.8601 What can you conclude? Х × ○ There is compelling evidence that the true average repair time exceeds 200 min. ● There is not compelling evidence that the true average repair time exceeds 200 min. (b) Using 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 ẞ(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.) ẞ(300) = 0.85 ×
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
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Transcribed Image Text:The article "Uncertainty Estimation in Railway Track Life-Cycle Cost"+ 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
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.
Ο Η: μ = 200
Haμ > 200
O Ho: μ = 200
Ha: <200
O Ho: M = 200
Haμ 200
Ο Ηρ: μ > 200
Ha μ = 200
O Ho: μ<200
Ha: μ = 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 = 0.18
P-value = 0.8601
What can you conclude?
Х
×
○ There is compelling evidence that the true average repair time exceeds 200 min.
● There is not compelling evidence that the true average repair time exceeds 200 min.
(b) Using 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 ẞ(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.)
ẞ(300) = 0.85
×
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