Section Exercises
One-Way ANOVA
Use the following information to answer the next five exercises. There are five basic assumptions that must be fulfilled in order to perform a one-way ANOVA test. What are they?
1. Write one assumption.
3. Write a third assumption.
5. Write the final assumption.
7. State the alternative hypothesis for a one-way ANOVA test if there are three groups.
9. Three different traffic routes are tested for mean driving time. The entries in the table are the driving times in minutes on the three different routes. The one-way ANOVA results are shown in Table.
| Route 1 | Route 2 | Route 3 |
|---|---|---|
| 30 | 27 | 16 |
| 32 | 29 | 41 |
| 27 | 28 | 22 |
| 35 | 36 | 31 |
10. State SSbetween, SSwithin, and the F statistic.
| Northeast | South | West | Central | East | |
|---|---|---|---|---|---|
| 16.3 | 16.9 | 16.4 | 16.2 | 17.1 | |
| 16.1 | 16.5 | 16.5 | 16.6 | 17.2 | |
| 16.4 | 16.4 | 16.6 | 16.5 | 16.6 | |
| 16.5 | 16.2 | 16.1 | 16.4 | 16.8 | |
| [latex]\overline{x}[/latex]= | ________ | ________ | ________ | ________ | ________ |
| [latex]{s}_{2}[/latex]= | ________ | ________ | ________ | ________ | ________ |
12. State the hypotheses.
H0: ____________
Ha: ____________
The F Distribution and the F-Ratio
Use the following information to answer the next eight exercises. Groups of men from three different areas of the country are to be tested for mean weight. The entries in the table are the weights for the different groups. The one-way ANOVA results are shown in Table.
| Group 1 | Group 2 | Group 3 |
|---|---|---|
| 216 | 202 | 170 |
| 198 | 213 | 165 |
| 240 | 284 | 182 |
| 187 | 228 | 197 |
| 176 | 210 | 201 |
13. What is the Sum of Squares Factor?
15. What is the df for the numerator?
17. What is the Mean Square Factor?
19. What is the F statistic?
| Team 1 | Team 2 | Team 3 | Team 4 |
|---|---|---|---|
| 1 | 2 | 0 | 3 |
| 2 | 3 | 1 | 4 |
| 0 | 2 | 1 | 4 |
| 3 | 4 | 0 | 3 |
| 2 | 4 | 0 | 2 |
20. What is SSbetween?
21. What is the df for the numerator?
23. What is SSwithin?
25. What is MSwithin?
27. Judging by the F statistic, do you think it is likely or unlikely that you will reject the null hypothesis?
| Northeast | South | West | Central | East | |
|---|---|---|---|---|---|
| 16.3 | 16.9 | 16.4 | 16.2 | 17.1 | |
| 16.1 | 16.5 | 16.5 | 16.6 | 17.2 | |
| 16.4 | 16.4 | 16.6 | 16.5 | 16.6 | |
| 16.5 | 16.2 | 16.1 | 16.4 | 16.8 | |
| [latex]\overline{x}[/latex]= | ________ | ________ | ________ | ________ | ________ |
| [latex]{s}_{2}[/latex] | ________ | ________ | ________ | ________ | ________ |
28. H0: µ1 = µ2 = µ3 = µ4 = µ5
29. Hα: At least any two of the group means µ1, µ2, …, µ5 are not equal.
30. degrees of freedom – numerator: df(num) = _________
31. degrees of freedom – denominator: df(denom) = ________
Facts About the F Distribution
33. An F statistic can have what values?
34. What happens to the curves as the degrees of freedom for the numerator and the denominator get larger?
| Team 1 | Team 2 | Team 3 | Team