The article "Uncertainty Estimation in Railway Track...

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. $\begin{array}{lllllllllll}{159} & {120} & {480} & {149} & {270} & {547} & {340} & {43} & {228} & {202} & {240} & {218}\end{array}$ 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. Is there compelling evidence for concluding that true average repair time exceeds 200 $\mathrm{min}$ ? Carry out a test of hypotheses using a significance level of $.05 .$

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.
$\begin{array}{lllllllllll}{159} & {120} & {480} & {149} & {270} & {547} & {340} & {43} & {228} & {202} & {240} & {218}\end{array}$
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. Is there compelling evidence for concluding
that true average repair time exceeds 200 $\mathrm{min}$ ? Carry out a test of hypotheses using a significance level of $.05 .$

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Key Concepts

Hypothesis Testing

This concept involves formulating a null hypothesis and an alternative hypothesis, then using sample data to decide whether there is sufficient evidence to reject the null hypothesis. In the context of assessing mean repair times, it is central to determining if the true average exceeds a specified value.

One?Sample t-Test

When the underlying population is assumed to be normally distributed and the sample size is relatively small, the one-sample t-test is used to test hypotheses about the mean. It utilizes the sample mean and standard deviation to compute a test statistic that follows a t-distribution with n-1 degrees of freedom.

Normal Distribution Assumption

Assuming that the population distribution is approximately normal is key in the context of using the t-test, as it justifies the use of the t-distribution for inference on the population mean. This assumption is typically checked through graphical methods like a normal probability plot.

Significance Level

The significance level, typically denoted by alpha (?), represents the probability of rejecting the null hypothesis when it is actually true (Type I error). It is a crucial threshold in hypothesis testing that determines the stringency of the evidence required to conclude that the true mean exceeds a specific value.

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