Question

The heating bills for a selected sample of houses in five different cities using various forms of heating are given below (values are in dollars).

City	Gas Heated Homes	Central Electric	Heat Pump
Ankara	83	90	81
Konya	80	88	83
Çorum	82	87	80
Yozgat	83	82	82
Kırşehir	82	83	79

1. Is there a significant difference among the average bills of the homes according to the different heating methods? Test at 10% significance level by using one-way ANOVA method. (hint: using excel data analysis option (data/data analysis)).

1. What is the proper null hypothesis?
2. What is the proper alternative null hypothesis?
3. What is the value that represents the between group variation?
4. What is the value that represents the F ratio?
5. What is the value that represents the F critical?
6. What is your decision?

2. Is there a significant difference among the average bills of the homes according to the different cities? Test at 10% significance level by using one-way ANOVA method. (hint: using excel data analysis option (data/data analysis)).

1. What is the proper null hypothesis?
2. What is the proper alternative null hypothesis?
3. What is the value that represents the between group variation?
4. What is the value that represents the F ratio?
5. What is the value that represents the F critical?
6. What is your decision?

3. Prepare two-way ANOVA to repeat the tests at 10% significance level. (hint: using excel data analysis option (data/data analysis)).

1. What is the value that represents the F ratio for the test of equality of bills according to heating methods?
2. What is the value that represents the F ratio for the test of equality of bills according to cities?

(Note: If “data analysis” OPTION not loaded follow the below instructions to load)

Click àFile (or office button)

Choose à options

Choose à add-ins

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Mark à Analysis toolpack-VBA

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When you click data tab you should see “data analysis” at the upper right corner of the tool bar.

Answer 1

Answer 1.

a. Null Hypothesis, Ho; There is no significant difference among the average bills of the homes according to the different heating methods, i.e.

b. Alternative Hypothesis, Ha: There exists at least one heating method for which the average bill of homes is significantly different, i.e. there exists at least one for at least one

c. Between Group Variation = Sum of Squares Between Group = 70

d. F- ratio = 6.7742

e. F-critical = 2.8068

f. Since, F-ratio > F-critical, we Reject Ho at 10% level of significance and conclude that There exists at least one heating method for which the average bill of homes is significantly different, i.e. there exists at least one for at least one

Answer 2.

a. Null Hypothesis, Ho; There is no significant difference among the average bills of the homes across different cities, i.e.

b. Alternative Hypothesis, Ha: There exists at least one city for which the average bill of homes is significantly different, i.e. there exists at least one for at least one

c. Between Group Variation = Sum of Squares Between Group = 19.3333

d. F- ratio = 0.42899

e. F-critical = 2.6053

f. Since, F-ratio < F-critical, we fail to Reject Ho at 10% level of significance and conclude that There is no significant difference among the average bills of the homes across different cities, i.e.

Answer 3.

Answer a. F ratio for the test of equality of bills according to heating methods = Sum of Squares due to Columns = 6.5625

Answer b.  F ratio for the test of equality of bills according to cities = Sum of Squares due to Rows = 0.90625