Question

4) Finally, you wish to determine if the mean monthly sales of the shirt in the superstores that comprise part of the chain in four regions of the country that you have defined differ from each other. Random samples of the sales of the item in stores chosen from each region are selected. The sample data comprising these sales figures is shown in appendix four below. At the 1% level of significance, are there any differences in the mean monthly sales of the item in the populations of superstores in the four regions of the country? If you do observe that there are differences in the mean monthly sales of the shirt, perform the necessary additional test to ascertain which pairs of stores exhibit different mean sales at the 1% level of significance. Perform the appropriate test to show whether the desired property of homogeneity of variances exists for this study, also at the 1% level of significance

Region

   Store                 One                Two                Three             Four               

      1                      459                 282                 545                 490

      2                      490                 355                 588                 402

      3                      421                 348                 496                 397

      4                      500                 389                 439                 440

      5                      489                 276                 476                 501

      6                      540                 430                 510                 375

      7                      555                 387                 519                 398

            8                      421                 411                 483                 490

            9                      489                 443                 311                 355

         10                     551                 477                 390                 439

         11                     490                 398                 430                 503

         12                     401                 375                 275                 622

Q_{.01,4, 44} = 4.68                                       

Answer 1

One-way ANOVA: Sales versus Store

Source	DF	SS	MS	F	P
Store	3	68801	22934	4.53	0.007
Error	44	222800	5064
Total	47	291601

Comment: The estimated p-value is 0.007 and less than 0.01 significance level. hence, at the 1% level of significance, there are at least two regions of the country has significant mean monthly sales of the item in the populations.

From both the test statistics, the p-values are more than 0.01 significance level. Hence, we can conclude that the desired property of homogeneity of variances exists for this study.