Testing a Claim about a Difference between Means — Quiz
Question 8 • Statistics
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 point 5 inches. The mean height of the sample of college male basketball players is 74 point 5 inches with a standard deviation of 5 point 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. Let mu sub 1 is equal to the true mean height of all professional male basketball players and mu sub 2 is equal to the true mean height of all college male basketball players. What are the appropriate hypotheses?
Answer
A
ratio of cap h sub 0 to mu sub 1 minus mu sub 2 is equal to 0 , ratio of cap h sub A to mu sub 1 minus mu sub 2 is greater than 0
B
ratio of cap h sub 0 to mu sub 1 minus mu sub 2 is greater than 0 , ratio of cap h sub A to mu sub 1 minus mu sub 2 is equal to 0
C
ratio of cap h sub 0 to mu sub 1 minus mu sub 2 is less than 0 , ratio of cap h sub A to mu sub 1 minus mu sub 2 is equal to 0
D
ratio of cap h sub 0 to mu sub 1 minus mu sub 2 is equal to 0 , ratio of cap h sub A to mu sub 1 minus mu sub 2 is less than 0
Explanation
The claim is that professional players have a greater true mean height than college players, so the alternative hypothesis is μ₁ − μ₂ > 0. The null hypothesis represents no difference in the population means, so μ₁ − μ₂ = 0. This matches choice A: H₀: μ₁ − μ₂ = 0 and Hₐ: μ₁ − μ₂ > 0.
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