A gym teacher uses three exercises to increase arm strength: push-ups, pull-ups, and rope climbing. He has 10 students in small class. The exercises consist of doing as many push-ups as possible in 2 minutes. After a rest the student does as many push-ups as possible in 2 minutes. After a rest the student climbs a rope and the time is recorded in seconds. The data for this class is given below. Test the null hypothesis that all coefficients are zero at the 95% confidence level.
Push-ups
| Pull-ups
| Rope
Climb | | Push-ups
| Pull-ups
| Rope
Climb |
| 16 | 13 | 69 | | 17 | 19 | 68 |
| 18 | 20 | 56 | | 23 | 22 | 49 |
| 24 | 25 | 46 | | 21 | 21 | 52 |
| 22 | 18 | 59 | | 20 | 16 | 63 |
| 19 | 15 | 65 | | 16 | 17 | 74 |
◦ The probability plot of residuals indicates normality of residuals so the hypothesis test is inconclusive.
◦ Reject the null hypothesis.
◦ The probability plot of residuals indicates non-normality of residuals so the hypothesis test is inconclusive.
◦ Fail to reject the null hypothesis.
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