A researcher claims that a post-lunch nap decreases the amount of time it takes males to sprint 20 meters after a night with only 4 hours of sleep. The table shows the amounts of time (in seconds) it took for 10 males to sprint 20 meters after a night with only 4 hours of sleep when they did not take a post-lunch nap and when they did take a post-lunch nap. At α = 0.01, is there enough evidence to support the researcher’s claim?

(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.

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Male Sprint time (without nap) 4.07 3.94 3.92 3.97 3.92 Sprint time(with nap) 33 3.87 3.85 3.92 3.90 Male Sprint time (without nap) 396 4.07 3.93 3.99 4.02 Sprint time(with nap) 6 7 89 10 3.85 3.92 3.80 3.89 3.89