AnswersProbability and Statistics with Applications Honors Sem-2-FL-1210300 2024-2025Testing a Claim about a Population ProportionQuestion 10
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Testing a Claim about a Population Proportion

Question 10 • Probability and Statistics with Applications Honors Sem-2-FL-1210300 (2024-2025)

According to a soccer coach, 75% of soccer players have had at least one sprained ankle. An athletic trainer would like to investigate this claim. To do so, the trainer selects a random sample of 125 college soccer players from across the country and finds that 99 of them have had at least one sprained ankle. The trainer would like to know if the data provide convincing evidence that the true proportion of college soccer players who have had at least one sprained ankle is greater than 75%. Are the conditions for inference met for conducting a z-test for one proportion?

Answer
A
Yes, the random, 10%, and large counts conditions are all met.
B
No, the random condition is not met.
C
No, the 10% condition is not met.
D
No, the large counts condition is not met.

Explanation

The sample was selected randomly, so the random condition is met. The sample of 125 players is less than 10% of all college soccer players, so the 10% condition is met. For the large counts condition, use the claimed proportion of 0.75: the expected counts are 125(0.75) = 93.75 with an ankle sprain and 125(0.25) = 31.25 without one, both at least 10. Therefore, the conditions are met; the correct choice is “Yes, the random, 10%, and large counts conditions are all met.”

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