A large group of workers is divided into three departments: special operations, the main floor, and management. Strep throat has been spreading, and a health inspector wants to know if there is a relationship between department and having strep throat. She selects a random sample of 100 workers and classifies each one according to their department and whether they have strep throat. The responses are displayed in the table.

The health inspector would like to know if these data provide convincing evidence that the distribution of strep throat status differs across the departments in the population of all workers at this large company. Are the conditions for inference met?

A. No, the random condition is not met.
B. No, the 10% condition is not met.
C. No, the Large Counts condition is not met.
D. Yes, all three conditions for inference are met.

Large counts: The number of successes and failures in each category must be large enough so that the sampling distribution of the sample proportion is approximately normal.

Independence: The observations in the sample must be independent of each other. In this case, the data was collected from a random sample of 100 workers. The number of successes and failures in each category is large enough (at least 10 in each category). And there is no reason to believe that the observations in the sample are not independent of each other.

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