Question

Employees at a regional hospital spend an average of $7 per day on lunch, with a standard deviation $4. A simple random sample of 100 employees is studied. What is the expected value of the sampling distribution of the sample mean?

Answer 1

The expected value of the sampling distribution of the sample mean for hospital employees' lunch expenses is the population mean, which is $7.

Step-by-step explanation:

The student's question pertains to the concepts of sampling distributions and expected value in statistics, specifically within the context of the Central Limit Theorem. The expected value of the sampling distribution of the sample mean is simply the population mean because the distribution of sample means will be centered around the population mean when the sample size is sufficiently large. As the employees at a regional hospital spend an average of $7 per day on lunch, this is the mean of the population. Therefore, the expected value of the sampling distribution of the sample mean, even when taken from a simple random sample of 100 employees, is also $7.