Homework SourseYou take a sample of 3 items of each of four different brand
You take a sample of 3 items of each of four different brands. Can you conclude that the mean values of all four brands are equal?
| A | B | C | D |
|---|---|---|---|
| 20 | 25 | 24 | 23 |
| 19 | 23 | 20 | 20 |
| 21 | 21 | 22 | 20 |
Solution
Since here we want to compare the more than 2 means so one way ANOVA will be used. Hypotheses are:
H0: Mean of all the brands are same.
Ha: Mean of all the brands are not same.
Analysis shows that the F statistics is
F= 1.667
And p-value is : 0.2503
Since p-value is greater than 0.05 so we fail to reject the null hypothesis at 5%. That is on the basis of sample evidence we can conclude that the mean values of all four brands are equal.
| Anova: Single Factor | ||||||
| SUMMARY | ||||||
| Groups | Count | Sum | Average | Variance | ||
| A | 3 | 60 | 20 | 1 | ||
| B | 3 | 69 | 23 | 4 | ||
| C | 3 | 66 | 22 | 4 | ||
| D | 3 | 63 | 21 | 3 | ||
| ANOVA | ||||||
| Source of Variation | SS | df | MS | F | P-value | F crit |
| Between Groups | 15 | 3 | 5 | 1.666667 | 0.250324 | 4.066181 |
| Within Groups | 24 | 8 | 3 | |||
| Total | 39 | 11 |
