A health spa claims that a new exercise program will reduce a person's waist size by 2 centimeters on average over a five-day period. The waist sizes, in centimeters, of 6 men who participated in this program were recorded before and after the 5-day period.

| Man | Waist Size Before (cm) | Waist Size After (cm) |
|-----|------------------------|-----------------------|
| 1 | 90.4 | 91.7 |
| 2 | 95.5 | 93.9 |
| 3 | 98.7 | 97.4 |
| 4 | 115.9 | 112.8 |
| 5 | 104.0 | 101.3 |
| 6 | 85.6 | 84.0 |

State the null and the alternative hypotheses.

The null hypothesis is that the new exercise program won't reduce waist sizes (μ = 0). The alternative hypothesis is that the exercise program will reduce waist sizes (μ < 0).

Explanation:

The question relates to statistical hypothesis testing. In this scenario, the null hypothesis (H0) would be that the exercise program does not reduce waist sizes. Mathematically, this can be stated as μ = 0 where μ is the average change in waist size. The alternative hypothesis (H1) would be that the exercise program does reduce waist sizes, or μ < 0. These hypotheses are established based on the claim made by the health spa that the exercise program will reduce waist size by average 2 centimeters over a five day period.

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