Question 3 • Probability and Statistics with Applications Honors Sem-2-FL-1210300 (2024-2025)
A varsity swimmer at a large high school wants to estimate the amount of time (in hours), on average, athletes at this school train or practice each day. This swimmer selects 10 members of her swim team and asks them how many hours they typically train or practice. Use the data to construct a 90% confidence interval to estimate the true mean number of hours athletes at this school train or practice each day.0.5, 1, 1, 2, 2, 2, 2.5, 2.5, 3, 3
Answer
A
No, the sample is not random.
B
No, the graph of the data shows skewness and has outliers.
C
No, the 10% condition cannot be verified, because it is not known how many seniors are in the population.
D
Yes, the student selected a random sample; 10 is less than 10% of the population of athletes, and the graph of the data shows no clear skewness or outliers.
Explanation
The 10 students were selected from the swimmer’s own swim team, not randomly from all athletes at the school. That creates a selection bias: swim team members may train more or differently than athletes in other sports. Since a representative random sample is needed for a confidence interval to estimate the school-wide mean, the correct choice is “No, the sample is not random.”
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