159%
Module 13: F-Distribution and One-Way ANOVA
Module 13: F-Distribution and One-Way ANOVA
Section Exercises
Barbara Illowsky & OpenStax et al.
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?
| 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 |
17. What is the Mean Square Factor?
| 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 |
| 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) = _________
Facts About the F Distribution
| Team 1 | Team 2 | Team 3 | Team 4 | Team 5 |
|---|---|---|---|---|
| 36 | 32 | 48 | 38 | 41 |
| 42 | 35 | 50 | 44 | 39 |
| 51 | 38 | 39 | 46 | 40 |
| Group A | Group B | Group C |
|---|---|---|
| 101 | 151 | 101 |
| 108 | 149 | 109 |
| 98 | 160 | 198 |
| 107 | 112 | 186 |
| 111 | 126 | 160 |
48. At the 10% significance level, are the scores among the different groups different?
| 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]= | ________ | ________ | ________ | ________ | ________ |
49. Enter the data into your calculator or computer.
State the decisions and con