Suppose that two very large companies (A and B) each select random samples of th

Question

Suppose that two very large companies (A and B) each select random samples of their employees. Company A has 5000 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 company randomly selects 50 employees for the survey, which of the following is true about the sampling distributions of the sample means (the mean number of sick days)? Assume the variability in number of sick days to be the same for both companies. The sampling distributions of the sample means will have about the same standard deviation. The standard deviation for a sampling distribution of a sample mean depends only on the sample size, not the population (company) size. Since Company A is surveying a higher percent of its employees, the standard deviation of the sampling distribution for its sample mean will be smaller than that for Company B (the larger company). Larger companies should take larger samples. Since Company B is a larger company, the standard deviation for its sampling distribution of the sample mean is smaller. The larger a population, the smaller the standard deviation of a sample mean's sampling distribution. None of the answers are correct.

Explanation / Answer

The sampling distribution of sample means will have about same standard deviations . The standard deviation of sample mean depends on sample size not the population size.

The standard deviation of sample mean is given by

Population standard deviation/ sqrt n

Since n , the sample size same for both the samples and population standard deviation same

So standard deviation of sample mean same

Note: for finite population of size N

Standard deviation of sample mean is given by

(Population s.d/sqrt n)* sqrt( (N-n)/( N-1))

Which doesn't make much difference

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