Suppose that two very large companies, A and B, each select random samples of their employees. Company A has 5,000 employees and Company B has 15,000 employees. In both surveys, the company will record the number of sick days taken by each sampled employee. If each firm randomly selects 3% of its employees, which statement is true about the sampling distributions of the sample means? The smaller company, Company A, will have a sampling distribution with smaller standard deviation. None of the answer options are correct. The standard deviation of the sampling distribution of the sample mean will be smaller for the larger company, Company B, because a larger sample is being selected. The sampling distributions of the sample means will have about the same standard deviation because, in both cases, we’re selecting 3% of the employees.

Options

The smaller company, Company A, will have a sampling distribution with smaller standard deviation.

None of the answer options are correct.

The standard deviation of the sampling distribution of the sample mean will be smaller for the larger company, Company B, because a larger sample is being selected.

The sampling distributions of the sample means will have about the same standard deviation because, in both cases, we’re selecting 3% of the employees.

The standard deviation of the sampling distribution of the sample mean will be smaller for the larger company, Company B, because a larger sample is being selected.

Step-by-step explanation:

Given

Company A = 5000 employees

Company B = 15,000 employees

Selection for both companies = 3%

Note that:

The larger the sample size, the smaller the variance of the sampling distribution of the mean

For company A;

3% of 5000 were selected = 150

For company B

3% of 15000 were selected = 450

Since 450 (B) is greater than 150 (A) then then the standard deviation of the sampling distribution of the sample mean will be smaller for the larger company (Company B) because a larger sample (450) is selected