Question

Performance of a bus depot. Refer to the International Journal of Engineering Science and Technology (February 2011) study of public bus depot performance, Exercise 9.25 (p. 544). Recall that 150 customers provided overall performance ratings at each of three different bus depots (Depot 1, Depot 2, and Depot 3). The average performance scores were determined to be significantly different at α=.05 using an ANOVA F-test. The sample mean performance scores were reported as . The researchers employed the Bonferroni method to rank the three performance means using an experiment wise error rate of .05. Adjusted 95% confidence intervals for the differences between each pair of treatment means are shown in the table. Use this information to rank the mean performance scores at the three bus depots.

Short answer

The rank is given by

Step-by-step solution

Given Information

The sample size is 150.

There are three treatments.

The level of significance is 0.05.

The 95% confidence interval for the difference between each pair of treatments means are given.

Bonferroni method

Bonferroni method does not require equal sample size. The Bonferroni method can be applied when pairwise comparisons are of interest. The formulas for constructing confidence intervals for difference between treatment means are given below

Ranking the mean performance

The means for treatment x₁ is 67.17.

The means for treatment x₂ is 58.69.

The means for treatment x₃ is 44.49.

Therefore, the rank is given by