At a gymnastics meet, three judges evaluate the balance beamperformances of five gymnasts. The judges use a scale of 1 to 10,where 10 is a perfect score. A statistician wants to examine thejobjectivity and consistency of the judges. Assume scores arenormally distrbuted.
| Judge 1 | Judge 2 | Judge 3 |
| Gymnast 1 | 8.0 | 8.5 | 8.2 |
| Gymnast 2 | 9.5 | 9.2 | 9.7 |
| Gymnast 3 | 7.3 | 7.5 | 7.7 |
| Gymnast 4 | 8.3 | 8.7 | 8.5 |
| Gymnast 5 | 8.8 | 9.2 | 9.0 |
- At the 1% significance level, can you conclude that averagescores differ by judge? Can you conclude that the judges seeminconsistent with thier scoring?
- At the 1% significance, can you conclude that average scoresdiffer by gymnast?
- If average scores differ by gymnast, use Tukey's HSD method atthe 1% significance level to determine which gymnasts' perfomrancesdiffer.
