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AssignmentMultiple Choice

Testing a Claim about a Mean Difference

Question 1 • Probability and Statistics with Applications Honors Sem-2-FL-1210300 (2024-2025)

Do the data provide convincing evidence at the α = 0.05 significance level that the new training program will change athletes’ resting heart rate for subjects like the ones in the experiment?Select the appropriate hypotheses for this scenario.

Answer
A
H0: μold = μnew ; Ha: μold ≠ μnew
B
H0: μdiff ≠ 0 ; Ha: μdiff = 0
C
H0: μdiff = 0 ; Ha: diff ≠ 0
D
H0: μdiff = 0 ; Ha: μdiff ≠ 0

Explanation

The question asks whether the program will change resting heart rate, so the alternative hypothesis must allow a difference in either direction. For paired measurements, define μdiff as the population mean change in heart rate. The null is no average change (μdiff = 0), and the alternative is a nonzero average change (μdiff ≠ 0), which is choice D.

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