Question 9 • Probability and Statistics with Applications Honors Sem-2-FL-1210300 (2024-2025)
A student claims that professional male basketball players are taller, on average, than college male basketball players. To investigate this claim, the student selects a random sample of 30 professional basketball players and 30 college basketball players. The mean height of the sample of professional male basketball players is 76 inches with a standard deviation of 3.5 inches. The mean height of the sample of college male basketball players is 74.5 inches with a standard deviation of 5.5 inches. The student would like to determine if there is convincing evidence that the true mean height of all professional male basketball players is greater than the true mean height of all college male basketball players.
Answer
A
H0: μ1 – μ2 = 0, Ha: μ1 – μ2 < 0
B
H0: μ1 – μ2 = 0, Ha: μ1 – μ2 > 0
C
H0: μ1 – μ2 < 0, Ha: μ1 – μ2 = 0
D
H0: μ1 – μ2 > 0, Ha: μ1 – μ2 = 0
Explanation
Let μ₁ be the true mean height of professional players and μ₂ the true mean height of college players. The claim that professional players are taller means μ₁ − μ₂ > 0, so this belongs in the alternative hypothesis. The null hypothesis represents no difference, μ₁ − μ₂ = 0. Therefore, choice B is correct.
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