Consider the set {1, 2, 3, 4}. a. Make a list of all samples of size 2 that can be drawn from this set of integers.
b. Construct the sampling distribution of sample means for samples of size 2 selected from this set.
c. Provide the distribution both in the form of a table and histogram.

(a)

(b) Sampling Distribution (Table)

(b) Sampling Distribution (Histogram)

See attachment

Step-by-step explanation:

Given

Solving (a): A list of sample size 2

We have:

--- the sample size

First, we calculate the number of list using permutation (orders matter)

So, we have:

And the list is:

Solving (b): Sample distribution  of sample means of (a)

First, calculate the mean of each set using:

So, we have:

Write out the sample means (sorted)

Construct a frequency table

Construct the sampling distribution where the probability is calculated using:

So, we have:

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