The article Uncertainty Estimation in Railway Track Life-Cycle Cost (J. of Rail and Rapid Transit, 2009) presented

Question:

The article "Uncertainty Estimation in Railway Track Life-Cycle Cost" (J. of Rail and Rapid Transit, 2009) 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
A normal probability plot of the data shows a reasonably linear pattern, so it is plausible that the population 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 .05.
b. Using σ = 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 β(300)?
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