An experiment is run to determine whether 4 brands of tires differ in terms of t

Question

An experiment is run to determine whether 4 brands of tires differ in terms of their tread wear over a period of 20,000 miles of driving.

Suppose the experiment is run with only 4 cars and that each brand of tires had been tested (in a random order) on each car for 20,000 miles, Complete the ANOVA to account for the change in the experimental design. Compare the treatment means and determine which Brand (or Brands) had the least wear at the 5% level of significance.

ANOVA for Tire Wear

Brand Rep 1 Rep 2 Rep 3 Rep 4 Rep 5 A 19 15 14 14 62 B 14 14 13 8 49 C 12 12 9 8 41 D 14 11 11 9 45 Total 59 52 47 39 197

Explanation / Answer

Brand C has least wear

Anova: Two-Factor Without Replication SUMMARY Count Sum Average Variance A 4 62 15.5 5.666666667 B 4 49 12.25 8.25 C 4 41 10.25 4.25 D 4 45 11.25 4.25 Rep 1 4 59 14.75 8.916666667 Rep 2 4 52 13 3.333333333 Rep 3 4 47 11.75 4.916666667 Rep 4 4 39 9.75 8.25 ANOVA Source of Variation SS df MS F P-value F crit Row 62.1875 3 20.72916667 13.26666667 0.00118415 3.862548358 Columns 53.1875 3 17.72916667 11.34666667 0.00205884 3.862548358 Error 14.0625 9 1.5625 Total 129.4375 15

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