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An apple juice manufacturer develops a new juice concentrate. This new product is a) more convenient, b) higher in quality, and c) less expensive than conventional apple juice. The marketing manager needs to decide whether advertising should stress convenience, quality, or price. A pilot study is done in three small cities each promoting one of the different attributes of the new juice concentrates. Then the mean sales for each city are compared. Does the approach to advertising affect sales? That is, is there a difference in the mean sales in the three cities? An ANOVA table, shown below provides the results of the sales surveys. Test at alpha = .01.
ANOVA table for one way analysis of variance:
Source of D.F. Sum of Squares Mean Square F-statistic
Treatment k-1 SST MST=SST/(k-1) F=MST/MSE
Error n-k SSE MSE=SST/(n-k)
Total n-1 SS(Total)
Source of D.F. Sum of Squares Mean Square F-statistic (calc.)
Treatment 2 57,512.2 28,756 3.23
Error 58 506,983.5 8,894
Total 60 564,495.7
Use the five-step hypothesis-testing procedure.
1. State the null hypothesis:
2. State the alternate hypothesis:
3. State the decision rule (I will reject the null hypothesis if the calculated value of the test statistic, F, is (greater than, or less than, or both)_______(then fill in the value)_______.
4. State the value of the test statistic
5. What is your decision regarding the null hypothesis (accept or reject)?
6. What does this say about advertising's affect on sales?
This solution gives the step by step method for ANOVA.