On a television show, eight contestants try to lose the highest percentage of weight in order to win a cash prize. As part of the show, the contestants are timed as they run an obstacle course. The table shows the times (in seconds) of the contestants at the beginning of the season and at the end of the season. At α = 0.01, is there enough evidence to support the claim that the contestants’ times have changed?

(a) Identify the claim and state H₀ and H_a,

(b) Find the critical value(s) and identify the rejection region(s),

(c) Calculate d̅ and s_d,

(d) Find the standardized test statistic t,

(e) Decide whether to reject or fail to reject the null hypothesis,

(f) Interpret the decision in the context of the original claim. Assume the samples are random and dependent, and the populations are normally distributed. If convenient, use technology.

Transcribed Image Text:

Contestant 1 Time (beginning) Time (end) 130.2 104.8 100.1 136.4 125.9 122.6 150.4 158.2 121.5 100.7 90.2 135.0 1121 120.5 139.8 142.9