In: Statistics and Probability
a shop sells three shoe brands. The shop owner wanted to find out if there were differences in sales levels of the three shoe brands. Therefore the store owner issued a monthly record of sales of the three shoe brands. With an error rate of 0.05, test whether there are differences in sales of the three shoe brands?
| 
 Month  | 
 I  | 
 II  | 
 III  | 
 IV  | 
 V  | 
 VI  | 
 VII  | 
| 
 Brand A  | 
 78  | 
 64  | 
 75  | 
 45  | 
 82  | 
 69  | 
 60  | 
| 
 Brand B  | 
 110  | 
 70  | 
 53  | 
 51  | 
 61  | 
 68  | 
|
| 
 Brand C  | 
 90  | 
 68  | 
 70  | 
 54  | 
 74  | 
 65  | 
 59  | 
Here, we are to test 
: there is no difference in the mean sales value of the 3 shoe
brands, versus, 
: the mean sales value of at least one of the 3 shoe brands is
different. We are to carry out a one-way Anova (Single Factor) test
for this purpose.
For Brand A, 
 = 7, 
 = 67.57, 
 = 158.95.
For Brand B, 
 = 6, 
 = 68.83, 
 = 465.37.
For Brand C, 
 = 7, 
 = 68.57, 
 = 134.62.
Also, overall mean = 68.30 = 
.

Since the test statistic value is less than the critical value, we
fail to reject the null hypothesis 
. We conclude that there is not enough evidence to suggest that
there are differences in sales of the three shoe brands.