A company director investigated whether there is a difference in the mean number of overtime hours worked each week by employees
assigned to two different managers. Each manager, A and B, manages 100 employees. Random samples of 35 employees from manager A and 40 employees from manager B were selected. The number of overtime hours worked was recorded for the 75 employees each week. Have the conditions been met for inference with a confidence interval for the difference in the population means?
Answer: C. No, because the size of at least one of the samples is greater than 10 percent of the population
To perform an inference with a confidence interval on a mean, certain conditions need to be met for the calculations to to be accurate.
Those conditions are that the sample should be RANDOM, NORMAL and INDEPENDENT.
This question concerns the Independence of the sample. In using this method, the observations should be independent of one another and the size of at least one of the samples should not be greater than 10% of the population.
Both the samples of manager A and manager B are in violation of this as they boast of 35 and 40 employees respectively which is higher than 10% of the 100 employee population.