Updated: <36> <37> Sara Lee recently developed a new cheesecake. The regional ma

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Updated:

<36>

<37>

Sara Lee recently developed a new cheesecake. The regional manager for Sara Lee would like to know if there is a difference in the mean number of cakes sold daily at Meijer stores in Sylvania, Northwood, and Maumee, denote these means by u1, u2 and u3, respectively. She selects a sample of days from each of the stores and finds the number of cakes sold on that day. The results are as follows Sylvania Northwood Maumee 14 10 17 12 12 16 13 13 17 12 11 18 17 The single factor Anova test in Excel was conducted at 5% significance level and the following incomplete Anova table is available Source SS DF MS Between 2 38.125 Groups Within Groups Total 86 12 What is the value of the mean squares due to error, MSE 9.75 1.645 0.975 39.1

Explanation / Answer

So that is thecomplete ANOVA Table

(a) So, Here MSE = 0.975, i calculated it from Excel but one can calculate it by dividing the Sum of Squares within the groups by the error degrees of freedom.

(b) In ANOVA, test statistic is F stats so here F = 39.10, which can be calculated by dividing the ratio of the Between Mean Sum of Squares to the Error Mean Sum of Squares

(c) p- value for the test = 1.87 * 10-5, which shows that test is outside 0.05 level of significance, so means are not equal for the groups.

(d) Null hypothesis is rejected if F value is the F test is lesser than Fcritical which is equal to 4.10 as per ANOVA table.so F>=4.10, so here null hypothesis is rejected as F value is quite higher is of 39 which is more than critical value of F, for alpha = 0.05 significance level.

(E) Our conclusion is option 3 that the avarage number cakes sold daily in three stores are not same.

Anova: Single Factor SUMMARY Groups Count Sum Average Variance Sylvania 4 51 12.75 0.916667 Northwood 4 46 11.5 1.666667 Maurnee 5 85 17 0.5 ANOVA Source of Variation SS df MS F P-value F crit Between Groups 76.25 2 38.125 39.10256 1.87E-05 4.102821 Within Groups 9.75 10 0.975 Total 86 12

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