In: Statistics and Probability
Finally, you wish to study whether the mean sales of various models of Nikon cameras that are sold by various stores differ from each other. Random samples of sales of the models of Nikon camera are selected. The data concerning the sales of these models are shown in appendix four below. At the 1% level of significance, are there any differences in the yearly mean sales of the models of Nikon camera in these populations of stores? If you do observe that there are differences in the mean sales of the camera models, at each of the levels of significance, perform the necessary additional test, using only PH stat in excel, to ascertain which mean sales differ from which other mean sales. Also, perform the appropriate test that illustrates whether, at each level of significance, the desired property of homogeneity of variances exists in this model.
Appendix Four: (Sales of Various Camera Models)
Camera Model
Store D5 D850 D7500 D7200
1 122 154 111 87
2 165 160 142 54
3 180 165 144 70
4 187 151 150 67
5 190 150 176 50
6 132 162 110 54
7 149 159 109 90
8 130 167 153 77
9 155 160 161 40
10 170 198 143 58
Hint: Q.01,4,36 = 4.74
The hypothesis being tested is:
H0: µ1 = µ2 = µ3 = µ4
Ha: At least one means is not equal
Mean | n | Std. Dev | |||
158.0 | 10 | 24.47 | D5 | ||
162.6 | 10 | 13.63 | D850 | ||
139.9 | 10 | 22.94 | D7500 | ||
64.7 | 10 | 16.40 | D7200 | ||
131.3 | 40 | 44.21 | Total | ||
ANOVA table | |||||
Source | SS | df | MS | F | p-value |
Treatment | 62,021.00 | 3 | 20,673.667 | 52.34 | 3.31E-13 |
Error | 14,219.40 | 36 | 394.983 | ||
Total | 76,240.40 | 39 |
The p-value is 0.000.
Since the p-value (0.000) is less than the significance level (0.01), we can reject the null hypothesis.
Therefore, we can conclude that there are differences in the mean sales of the camera models.
Tukey simultaneous comparison t-values (d.f. = 36) | |||||
D7200 | D7500 | D5 | D850 | ||
64.7 | 139.9 | 158.0 | 162.6 | ||
D7200 | 64.7 | ||||
D7500 | 139.9 | 8.46 | |||
D5 | 158.0 | 10.50 | 2.04 | ||
D850 | 162.6 | 11.01 | 2.55 | 0.52 | |
critical values for experimentwise error rate: | |||||
0.05 | 2.70 | ||||
0.01 | 3.35 |
There is a significant difference between D7200 and D850.
There is a significant difference between D7200 and D7500.
There is a significant difference between D7200 and D5.
There is a significant difference between D7500 and D850.
There is a significant difference between D7500 and D5.
Test for Equal Variances:
The hypothesis being tested is:
Null hypothesis | All variances are equal |
Alternative hypothesis | At least one variance is different |
Significance level | α = 0.05 |
95% Bonferroni Confidence Intervals for Standard Deviations
Sample | N | StDev | CI |
D5 | 10 | 24.4677 | (15.3135, 54.1107) |
D850 | 10 | 13.6317 | (8.5316, 30.1467) |
D7500 | 10 | 22.9417 | (14.3585, 50.7360) |
D7200 | 10 | 16.4049 | (10.2673, 36.2798) |
Method | Test Statistic |
P-Value |
Bartlett | 3.74 | 0.291 |
The p-value is 0.291.
Since the p-value (0.291) is greater than the significance level (0.01), we fail to reject the null hypothesis.
Therefore, we can conclude that all variances are equal.