Testing a Claim about a Difference between Means — Quiz
Question 1 • 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. The hypotheses 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 are tested, where 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. The conditions for inference have been met. The standardized test statistic is t is equal to 1 point 2 6 , and the cap p -value is between 0 point 1 0 and 0 point 1 5 What conclusion should be made using the significance level, alpha is equal to 0 point 0 5 ?
Answer
A
Reject cap h sub 0 . 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.
B
Reject cap h sub 0 . There is not 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.
C
Fail to reject cap h sub 0 . There is not 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.
D
Fail to reject cap h sub 0 . 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.
Explanation
The p-value is between 0.10 and 0.15, so it is greater than the significance level α = 0.05. Therefore, the result is not statistically significant, and we fail to reject the null hypothesis. There is not convincing evidence that professional male basketball players are taller on average than college male basketball players.
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