A random sample of 15 automobile mechanics certified to work

A random sample of 15 automobile mechanics certified to work on a certain type of car was selected, and the time (in minutes) necessary for each one to diagnose a particular problem was determined, resulting in the following data: 30.6 30.1 15.6 26.7 27.1 25.4 35.0 30.8 31.9 53.2 12.5 23.2 8.8 24.9 30.2 Use the Wilcoxon test at significance level 0.10 to decide whether the data suggests that true average diagnostic time is less than 30 minutes.

Solution

A random sample of 15 automobile mechanics certified to work on a certain type of car was selected, and the time (in minutes) necessary for each one to diagnose a particular problem was determined, resulting in the following data: 30.6 30.1 15.6 26.7 27.1 25.4 35.0 30.8 31.9 53.2 12.5 23.2 8.8 24.9 30.2 Use the Wilcoxon test at significance level 0.10 to decide whether the data suggests that true average diagnostic time is less than 30 minutes

MINITAB is used

Null hypothesis: true average diagnostic time is not less than 30 minutes

Alternate hypothesis: true average diagnostic time is less than 30 minutes

Wilcoxon Signed Rank Test: C1

Test of median = 30.00 versus median < 30.00

        N for   Wilcoxon         Estimated

     N   Test Statistic      P     Median

C1 15     15       39.0 0.122      27.55

Calculated P=0.122 which is > 0.10 level.

The null hypothesis is not rejected.

We conclude that true average diagnostic time is not less than 30 minutes.