Question

Suppose that a variable of a population has a reverse-J-shaped distribution and that two simple random samples are taken from the population.

a. Would you expect the distributions of the two samples to have roughly the same shape? If so, what shape?

b. Would you expect some variation in shape for the distributions of the two samples? Explain your answer.

Short answer

(a) The predicted shape of the two sample distributions is unchanged.

(B) The expected shape of the two sample distributions will differ.

Step-by-step solution

Part (a) Step 1: Given information

A variable of a population has a reverse-J-shaped distribution and that two simple random samples.

Part (a) Step 2: Explanation

A reverse-J-shaped distribution is assumed for a population variable, and two simple random samples are obtained from the population.

The majority of sample values taken from the population to create a simple random sample come from the middle of the distribution.

As a result, the shape of the two sample distribution should be roughly reverse-J-shaped.

As a result, the predicted shape of the two sample distributions is unchanged.

Part (b) Step 1: Given information

A variable of a population has a reverse-J-shaped distribution and that two simple random samples.

Part (b) Step 2: Explanation

A reverse-J-shaped distribution is assumed for a population variable, and two simple random samples are obtained from the population.

It is predicted that the basic random sample will have some variation. Although the two samples are drawn from the same population, it is unlikely that they will have the same set of observations.

As a result, the expected shape of the two sample distributions will differ.