Question 5 • 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. Let μ1 = the true mean height of all professional male basketball players and μ2 = the true mean height of all college male basketball players. Are the conditions for inference met?
Answer
A
No, the random condition is not met.
B
No, the 10% condition is not met.
C
No, the Normal/large sample condition is not met.
D
Yes, all of the conditions for inference have been met.
Explanation
The random condition is met because the student selected random samples from both groups. The 10% condition is reasonable because 30 players is less than 10% of the professional players and less than 10% of the college players. Each sample has 30 players, so the large-sample condition for comparing means is met; therefore, the conditions for inference are met. The correct choice is D, “Yes, all of the conditions for inference have been met.”
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