The heating bills for a selected sample of houses using various forms of heating are given below. (Values are in dollars.)
Natural Gas | Central Electric | Heat Pump |
84 | 95 | 85 |
64 | 60 | 93 |
93 | 89 | 90 |
88 | 96 | 92 |
71 | 90 | 80 |
a. | At α = 0.05, test to see if there is a significant difference among the average heating bills of the homes. Use the p-value approach. |
b. | Test the above hypotheses using the critical value approach. Let α = .05. |
a.
Source of Variation | SS | df | MS | F | P-value | F critical |
Between Groups | 173.33 | 2 | 86.667 | 0.656 | 0.537 | 3.885 |
Within Groups | 1586 | 12 | 132.167 | |||
Total | 1759.33 | 14 |
The test statistic F = 0.656; p-value > 0.1, do not reject Ho; we cannot conclude that there is a significant difference among the average heating bills (Excel results in a p-value of 0.5367)
b. F = 0.66 < 3.89; thus, do not reject Ho