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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?

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.

Answer :

Final answer:

The data for the trainer's z-test for one proportion meets all three main conditions: random, 10%, and large counts, which are required for inferential statistical analysis. The correct answer is option a.

Explanation:

The question pertains to whether the conditions for conducting a z-test for one proportion are met to determine if the true proportion of college soccer players who have had at least one sprained ankle is greater than 75%. This is a question of inferential statistics used to make judgments about a population based on a sample. To conduct a z-test, three main conditions must be met: random, 10%, and large counts conditions.

  • The random condition requires that the sample is randomly selected from the population, which is assumed to be true based on the information given.
  • The 10% condition applies when the sample size is less than 10% of the population. There are generally more than 1,250 college soccer players nationwide, so this condition is likely met.
  • The large counts condition requires that both the number of successes and failures in the sample are at least 10. With 99 having had a sprained ankle and 26 not, both numbers are greater than 10, so this condition is met.

Since all three conditions mentioned are met, the correct answer is: a. yes, the random, 10%, and large counts conditions are all met.

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