Question

A population of 1,000 students spends an average of $10.80 a day on dinner. The standard deviation of the expenditure is $4. A simple random sample of 64 students is taken.

What is the expected value (in dollars) of the sampling distribution of the sample mean?
What is the standard deviation (in dollars) of the sampling distribution of the sample mean? (Round your answer to four decimal places.).

Answer 1

The expected value of the sampling distribution of the sample mean is $10.80. The standard deviation of the sampling distribution of the sample mean is $0.50.

Step-by-step explanation:

To find the expected value of the sampling distribution of the sample mean, we can use the formula:

Expected Value of Sample Mean = Population Mean

In this case, the population mean is $10.80.

Therefore, the expected value of the sampling distribution of the sample mean is $10.80.

To find the standard deviation of the sampling distribution of the sample mean, we can use the formula:

Standard Deviation of Sample Mean = Population Standard Deviation / Square Root of Sample Size

In this case, the population standard deviation is $4 and the sample size is 64.

Therefore, the standard deviation of the sampling distribution of the sample mean is $4 / √64 = $4 / 8 = $0.50 (rounded to four decimal places).