Question

12-52.

A manufacturer of tortilla chips has recently developed a new product, a blue corn tortilla chip. The manufacturer has arranged with a regional supermarket chain to display the chips at the end of the aisle at four different locations in stores that have had similar weekly sales in snack foods. The dollar volumes of sales for the last six weeks in the four stores are as follows:

STORE
Week	1	2	3	4
1	$1,430.00	$980.00	$1,780.00	$2,300.00
2	$2,200.00	$1,400.00	$2,890.00	$2,680.00
3	$1,140.00	$1,200.00	$1,500.00	$2,000.00
4	$880.00	$1,300.00	$1,470.00	$1,900.00
5	$1,670.00	$1,300.00	$2,400.00	$2,540.00
6	$990.00	$550.00	$1,600.00	$1,900.00

a. If the assumptions of a one-way ANOVA design are satisfied in this case, what should the manufacturer conclude about the average sales at the four stores? Use a significance level of 0.05.

b. Discuss whether you think the assumptions of a one-way ANOVA are satisfied in this case and indicate why or why not. If they are not, what design is appropriate? Discuss.

c. Perform a randomized block analysis of variance test using a significance level of 0.05 to determine whether the mean sales for the four stores are different.

d. Comment on any differences between the means in parts b and c.

e. Suppose blocking was necessary and the researcher chooses not to use blocks. Discuss what impact this could have on the results of the analysis of variance.

f. Use Fisher’s least significant difference procedure to determine which, if any, stores have different true average weekly sales.

Answer 1

Hypothesis:

Null Hypothesis: All the mean sales at four stores are same.

Alternative Hypothesis: At least one mean sales of a store has significantly different from the remaining stores.

a)

One-way ANOVA: Sales versus Store

Source	DF	SS	MS	F	P-value
Store	3	4543500	1514500	7.66	0.001
Error	20	3956033	197802
Total	23	8499533

S = 444.7 R-Sq = 53.46% R-Sq(adj) = 46.47%

Comment: The estimated p-value is 0.001 and less than 0.05 level of significance. Hence, we reject the null hypothesis and conclude that at least one store has a significant mean sale at 0.05 level of significance.

b)

The assumption of normality on the error of the model can satisfy from the above plot. Because the estimated p-value is less than more than 0.05 level of significance.

c) Ans:

The estimated p-value of Bartlett's test for equal variance of sales at four stores is 0.506. Hence, we can conclude that the assumption of the equal variances at residual are satisfied at 0.05 level of significance.

d) The difference in b and c is that in c, we test the equality of mean sales at for stores whereas in d we test the equality of variances sales at four stores.

e)

The significance of mean sales at four stores may not be if the blocking was necessary and the researcher chooses not to use blocks. Becuase, the blocking reduces the sum of the square of error in the ANOVA table.

f)

Store 1 has significant mean sales with stores 3 and 4 at 0.05 level of significance.

Store 2 has significant mean sales with stores 3 and 4 at 0.05 level of significance.