23. Assume you are employed by a consumer-products rating service and your assig

Question

23. Assume you are employed by a consumer-products rating service and your assignment is to assess car batteries. For this part of your investigation, you want to determine whether there is a difference in

useful life among the top-of-the-line car batteries produced by three manufacturers (A, B, and C). To

provide the database for your assessment, you randomly sample four batteries from each manufacturer

and run them through laboratory tests that allow you to determine the useful life of each battery. The

following are the results given in months of useful battery life:

a. Use the analysis of variance with = 0.05 to determine whether there is a difference among these three brands of batteries.

b. Suppose you are asked to make a recommendation regarding the batteries based on useful life. Use the Tukey HSD test with = 0.05 to help you with your decision.

Explanation / Answer

Using ANOVA test in MS-EXCEL we get the following results.

(a)

Null Hypthesis: There is no differenece in the given three brands of batteries.

Since F value is greater than F critical we reject the null hypothesis , thus the evidence conclude that there should be difference among the given brand of batteries.

(b)

The results of tukey HSD test are,

Anova: Single Factor SUMMARY Groups Count Sum Average Variance A 4 227 56.75 2.916667 B 4 199 49.75 6.916667 C 4 198 49.5 15 ANOVA Source of Variation SS df MS F P-value F crit Between Groups 135.5 2 67.75 8.184564 0.009434 4.256495 Within Groups 74.5 9 8.277778 Total 210 11

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