A researcher claims that caffeine ingestion improves repeated freestyle sprints in trained male swimmers. The table shows the mean performance times (in seconds) for a group of trained male swimmers who complete six 75-meter maximal freestyle sprints after ingesting a placebo and after ingesting caffeine. 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 d and s_d, 

(d) Find the standardized test statistic t, 

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

(f ) interpret the decision in the context of the original claim. Assume the samples are random and dependent, and the populations are normally distributed.

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Sprint number 3 5 4 6. Sprint time (with placebo) 40.2 40.3 40.7 40.7 41.0 40.6 Sprint time (with caffeine) 39.9 39.7 40.1 40.5 39.9 40.2 2.