Stressed-Out Bus Drivers. Previous studies have shown tha urban bus drivers have an extremely stressful job, and a large pro portion of drivers retire prematurely with disabilities due to occupational stress. In the paper, "Hassles on the Job: A Study of a Job Intervention With Urban Bus Drivers" (Journal of Organizational Behavior, Vol. \(20\), pp. \(199-208)\), G. Evans et al. examined the effects of an intervention program to improve the conditions of urban bus drivers. Among other variables, the researchers monitored diastolic blood pressure of bus drivers in downtown Stockholm, Sweden. The data, in millimeters of mercury (mm Hg), on the WeissStats site are based on the blood pressures obtained prior to intervention for the \(41\) bus drivers in the study. Use the technology of your choice to do the following.

a. Obtain a normal probability plot, boxplot, histogram, and stemand-leaf diagram of the data.

b. Based on your results from part (a), can you reasonably apply the one-mean t-test to the data? Explain your reasoning.

c. At the \(10\%\) significance level, do the data provide sufficient evidence to conclude that the mean diastolic blood pressure of bus drivers in Stockholm exceeds the normal diastolic blood pressure of \(80mm\) Hg ?

We get the probability plot, box plot, histogram, and stem-and-leaf plot of the data using Minitab.

Stem-and-Leaf Display: PRESSURE

Leaf Unit =\(10\)

Stem

Here the sample size \(n=41\) is large. From the graphical representations we find that there Is outlier in the data. Hence, it is reasonable to use t-interval procedure on the given data.

Let the mean diastolic blood pressures of bus drivers in be denoted as $\mu$. The alternative and null hypotheses are both true.

${\mathrm{H}}_0:\mathrm{\mu }=80$mm Hg

${\mathrm{H}}_{\mathrm{a}}:\mathrm{\mu }>80$mm Hg

Significance level = \(10\%\) i.e.$\mathrm{\alpha }=0.1$

The population standard deviation is unknown in this situation. Therefore, we perform a t-test using MINITAB in the following approach:

Step 1: Press the Stat menu. Highlight the Basic statistics.

Step 2: Press \(1-\)sample t...

Step 3: Tick square Sample in columns: , and then enter the given data values

Sample in columns PRESSURE

('PRESSURE' is the variable name, given in the dataset)

\(80\) in the test (required for test)

Step 4: Select Options....and then input the data values provided.

Confidence level : \(90\)

Alternative greater than

Press ok twice

Using the above steps we find the \(P-\)value of the hypothesis test as \(P=0.141\)

Now,

Therefore, at \(10\%\) level of significance we do not reject the null hypothesis, ${\mathrm{H}}_0:\mathrm{\mu }=80\mathrm{mm}\mathrm{Hg}$

i.e, at \(10\%\) level of significance, the data do not provide sufficient evidence to conclude that the mean diastolic blood pressure of bus drivers in Stockholm exceeds the normal diastolic blood pressure of \(80mm\) Hg.