# The manager conducts a goodness-of-fit test to determine whether the proportions of workers of these types are identical to the population proportions of workers donating to charity, which are 50 percent for management, 30 percent for other white-collar workers, and 20 percent for blue-collar workers. Which of the following statements must be true about the sample? A) The expected number of blue-collar workers donating to charity is less than 30. B) The expected number of management workers donating to charity is 100. C) The expected numbers of other white-collar and blue-collar workers donating to charity are the same. D) The expected number of other white-collar workers donating to charity is 50. E) The combined expected numbers of other white-collar and blue-collar workers donating to charity is greater than the expected number of management workers donating to charity.

The manager conducts a goodness-of-fit test to determine whether the proportions of workers of these types are identical to the population proportions of workers donating to charity, which are 50 percent for management, 30 percent for other white-collar workers, and 20 percent for blue-collar workers. Which of the following statements must be true about the sample?

A) The expected number of blue-collar workers donating to charity is less than 30.

B) The expected number of management workers donating to charity is 100.

C) The expected numbers of other white-collar and blue-collar workers donating to charity are the same.

D) The expected number of other white-collar workers donating to charity is 50.

E) The combined expected numbers of other white-collar and blue-collar workers donating to charity is greater than the expected number of management workers donating to charity.

## Answer

Answer: B) The expected number of management workers donating to charity is 100.

Explanation: The expected number for each worker type is calculated based on the given proportions and the total sample size. For management workers, with 50% of the sample donating, the expected number is half of the total sample size.