Homework SourseThe heating bills for a selected sample of houses using vari
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
64
93
88
71
95
60
89
96
90
95
98
90
92
80
Below is the Sum of Squares for the between and within variation. Using this information, complete the table.
ANOVA Table
Source of Variation SS df MS F P-value
Between Groups 303.3 _ _ _ _
Within Groups 1565.0 _ _
Total 1959.3 _
At a=0.05, test to see if there is a significant difference among the average heating bills of homes. Use the p-value approach.
Test the above hypothesis using the critical value approach. Let a=.05.
If it turns out that there appears to be a difference, how would you determine which pair is different?
| Natural Gas | Central Electric | Heat Pump |
| 84 64 93 88 71 | 95 60 89 96 90 | 95 98 90 92 80 |
Solution
At a=0.05, test to see if there is a significant difference among the average heating bills of homes. Use the p-value approach.
Ho: there is no difference among the average heating bills of homes. (i.e. null hypothesis)
Ha:there is a signficant difference among the average heating bills of homes. (i.e. alternative hypothesis)
The test statistic is
F=1.1
The p-value of F test is 0.3645
Since the p-value is larger than 0.05, we do not reject the null hypothesis.
So we can not conclude that there is a signficant difference among the average heating bills of homes.
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Test the above hypothesis using the critical value approach. Let a=.05.
Ho: there is no difference among the average heating bills of homes. (i.e. null hypothesis)
Ha:there is a signficant difference among the average heating bills of homes. (i.e. alternative hypothesis)
The test statistic is
F=1.1
Given a=0.05, the critical value is F(0.95, df1=2, df2=12) =3.89 (from F table)
The rejection region is if F>3.89, we reject the null hypothesis.
Since F=1.1 is less than 3.89, we do not reject the null hypothesis.
So we can not conclude that there is a signficant difference among the average heating bills of homes.
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If it turns out that there appears to be a difference, how would you determine which pair is different?
Natural Gas and Heat Pump is different because the mean differences between these two groups are largest.
| Mean | n | Std. Dev | |
| 80.0 | 5 | 12.10 | Natural Gas |
| 86.0 | 5 | 14.85 | Central Electric |
| 91.0 | 5 | 6.86 | Heat Pump |
| 85.7 | 15 | 11.83 | Total |
