Question

1. Identify the correct statements. Fix the incorrect ones.

   1. A sampling distribution describes the distribution of data values.

   2. A sampling distribution shows the behavior of a sampling process over many samples.

   3. The probability distribution of a parameter is called a sampling distribution.

   4. Sampling distributions describe the values of a data summary for many samples.

Answer 1

The sampling distribution is nothing but the distribution of some statistic derived from sample values. Now the statistic is nothing but the summary of the data obtained in a sample. The value of the statistic depends on the sample values where the sample depends on the sampling process we adopt. Through the implementation of the specific sampling process several times, we generate the values of the statistic and then we distribute the whole probability '1' over the specific values taken by the statistic corresponding to the samples.

Therefore correct statements are:

The sampling distribution shows the behavior of a sampling process over many samples.

Sampling distributions describe the values of a data summary for many samples.

while the rests are Incorrect statements. Because the sampling distribution is the distribution of values of statistic rather than the individual sample values. Moreover the parameter is constant.Hence it does not have any distribution in case of a fixed population model.