A large group of workers is divided into three departments: special operations, main floor, and management. Strep throat has been going around, and a health inspector wants to know if there's a relationship between department and having strep throat.

She selects a random sample of 100 workers and classifies each according to their department and whether they have strep throat. The responses are displayed in a table.

The health inspector would like to know if these data provide convincing evidence that the distribution of strep throat status differs across departments in the population of all workers in 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.

The other condition is that there should not be more than 10 % condition of the sample size and this is achieved because 100 workers is less than the population.

The expected number of cases of strep throat in each department is :

Expected number of cases in special operations = (6 cases) / 3 departments = 2 cases

Expected number of cases in main floor = (13 cases) / 3 departments = 4 cases

Expected number of cases in management = (5 cases) / 3 departments = 1. 67 cases

The large counts condition is not met as the expected number of cases is not more than 5.

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