Question

Suppose a simple random sample of five hospitals is to be drawn from a population of 20 hospitals. There are 15{,}504 different samples of size 5 that can be drawn. The relative frequency distribution of the values of the mean of these 15{,}504 different samples would specify the _________ of the mean.

• A. sampling distribution
• B. normal distribution
• C. confidence interval
• D. confidence level

Hint:

All-possible-samples ⇒ sampling distribution; one sample ⇒ sample distribution.

Answer 1

The Correct Option is A

Step 1: What are we varying?
We enumerate all possible simple random samples of size $n=5$ from $N=20$ hospitals. The number of such samples is ${20 \choose 5}=15{,}504$, matching the stem.
Step 2: What distribution is formed?
For each possible sample we compute the sample mean. The distribution of these many sample means (across all possible samples) is by definition the sampling distribution of the mean.

Step 3: Eliminate distractors.
A normal distribution (b) is a specific shape; the sampling distribution may be approximately normal (CLT) but the stem asks what it is, not its shape.

A confidence interval (c) and a confidence level (d) are inferential constructs, not the distribution formed by all possible sample means. \[ \boxed{(a)} \]