Question

The math department at a small school has $5$teachers. The ages of these teachers are $23,34,37,42,58$. Suppose you select a random sample of $4$teachers and calculate the sample minimum age. Which of the following shows the sampling distribution of the sample minimum age?

a.

b.

c.

d.

e. None of these

Short answer

The correct option (c) i.e.

Step-by-step solution

Given information

We need to find the correct option showing the sampling distribution of the sample minimum age.

Explanation

We know that

The smallest age out of the four ages in the sample are

Sample of size four	Sample minimum
$23,34,37,42$	$23$
$23,34,37,58$	$23$
$23,34,42,58$	$23$
$23,37,42,58$	$23$
$34,37,42,58$	$34$

We then remark that the sample minimum sampling distribution should include $4$dots at $23$and $1$dot at $34$. (since there are $4$samples with sample minimum $23$and one sample with sample minimum $34$).

Therefore, the correct option is (c) i.e.