Question

Choose the correct option for the following question given below:
Since the population size is always larger than sample size, then the sample statistic-
A. Can never be larger than the population parameter.
B. Can never be equal to the population parameter.
C. Can never be zero.
D. Can never be smaller than the population parameter.
E. None of the above answers are correct.

Answer 1

By the process of elimination, take into consideration all the options, then define them. Relate it to the question and choose the correct option from the definition by eliminating all the wrong answers.

Complete step-by-step solution:
A parameter is a value that describes the entire population’s characteristics such as the population mean, median and mode including variance of the population. Since you cannot measure the entire population, you consider taking a parameter. A statistic is a characteristic of a sample. These characteristics of a sample can be the standard deviation and mean.
The sample statistic will be depending on the sample you choose.
It can be less than the population parameter.
It can be greater than the population parameter.
It can be equal to the population parameter.
It can also assume the value of zero.
Hence, none of the options are correct.

$\therefore$ The correct option is E.

Note: We can observe that from the solution of the question, a population includes all members from a specified group, all possible outcomes or measurements that are of interest. The exact population will depend on the scope of the study. And then, a sample consists of some observations drawn from the population, so a part or a subset of the population. The sample is the group of elements who actually participated in the study. Hence, a sample is a subset of a population, a sample always smaller than the population.