15.4 A manufacturer of cereal is considering three alternative box colors—red, yellow, and blue. To check whether such a consideration has any effect on sales, 16 stores of approximately equal size are chosen. Red boxes are sent to 6 of these stores, yellow boxes to 5 others, and blue boxes to the remaining 5. After a few days a check is made on the number of sales in each store. The results (in tens of boxes) shown in the following table were obtained.

Red Yellow Blue 43 52 61 52 37 29 59 38 38 76 64 53 61 74 79 81

a. Calculate the within-groups, between-groups, and total sum of squares.

b. Complete the analysis of variance table, and test the null hypothesis that the population mean sales levels are the same for all three box colors.