You are apart-time crew at a fast food chain. Suppose you serve a certain number of customers every hour.

Question

You are apart-time crew at a fast food chain. Suppose you serve a certain number of customers every hour. Assume the number of people you have served in 3 hours and let this be your population (choose three numbers only). Assume that samples of size n=2 are randomly selected without replacement from the population. Find the population mean μ and the mean μ_x ̅ of the sampling distribution of the means.

Is this correct?

A. Population: 12, 14,16 (n=3)

B. Population Mean: 14

What is the?

C. Means of Samples Drawn without Replacement from the Population

Observation	Sample	x ̅

and

Mean of the Sampling Distribution of the Sample Mean:

Answer 1

Using the population you described in part A, then the population mean calculated in part B is correct.

I've filled in the middle column with three samples (each of size n = 2). We cannot use a sample that repeats the number (e.g. 12,12) because samples are drawn without replacement.

The third column is the mean for each of the samples drawn/listed in the middle column.

A. Population: 12, 14,16 (n=3)

B. Population Mean: 14

C. Means of Samples Drawn without Replacement from the Population

Observation	Sample	x ̅
	12, 14	13
	14, 16	15
	12, 16	14

and

Mean of the Sampling Distribution of the Sample Mean:

This is the mean of all the numbers in the third column (i.e. the mean of the means)

(13 + 15 + 14)/3 = 14