Question 23 • Probability and Statistics with Applications Honors Sem-2-FL-1210300 (2024-2025)
A random sample of 30 professional tennis players is selected. For each tennis player, their first serve percentage and their second serve percentage are recorded. A 95% confidence interval for the mean difference (first – second) in serve percentages is found to be 0.10 to 0.18. A tennis coach claims that there is no difference in first and second serve percentages among professional tennis players. Is this claim supported by the confidence interval?
Answer
A
No, the confidence interval does not contain the value of 0.
B
Yes, the confidence interval does not contain the value of 0.
C
No, the confidence interval does not contain negative numbers.
D
Yes, the confidence interval consists entirely of positive numbers.
Explanation
A claim of no difference means the mean difference (first serve percentage − second serve percentage) is 0. The 95% confidence interval is 0.10 to 0.18, which does not include 0, so the interval does not support the coach’s claim. The correct choice is “No, the confidence interval does not contain the value of 0.”
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