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.