In a study aimed at comparing the average tread lives of four types of truck tires, 28 trucks were randomly divided into four groups of seven trucks. Each group of seven trucks was equipped with tires from one of the four types. The data in TireLife1 Way.txt consist of the average tread lives of the four tires of each truck.
(a) Are there any differences among the four types of tires? State the relevant null and alternative hypotheses for answering this question. Use either hand calculations or R commands to conduct the ANOVA F test at level of significance α = 0.1, and state any assumptions that are needed for the validity of this test procedure. (Hint. If you choose hand calculations, you may use the following summary statistics:
(b) It is known that tire types 1 and 2 are brand A tires, while tire types 3 and 4 are brand B tires. Of interest is to compare the two brands of tires.
(i) Write the relevant contrast, and the null and alternative hypotheses to be tested for this comparison. (ii) Use either hand calculations or R commands similar to those given in Example 10.2-2 to conduct the test at α = 0.1 and to construct a 90% CI.
(iii) Is the outcome of the test for the specialized contrast in agreement with the outcome of the test for the overall null hypothesis in part (a)? If not, provide an explanation.
Example 10.2-2
A quantification of coastal water quality converts measurements on several pollutants to a water quality index with values from 1 to 10. An investigation into the after-clean-up water quality of a lake focuses on five areas encompassing the two beaches on the eastern shore and the three beaches on the western shore.