Question

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

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.

H₀: μ > 200
H_a: μ = 200H₀: μ = 200
H_a: μ < 200    H₀: μ < 200
H_a: μ = 200H₀: μ = 200
H_a: μ ≠ 200H₀: μ = 200
H_a: 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	=
P-value	=

What can you conclude?

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

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)? (Round your answer to two decimal places.)
β(300) =

Answer 1

Conclusion:

There is not compelling evidence that the true average repair time exceeds 200 min.    

b) Here null hypothesis H0 is true. So, there will be no type II error