91Ó°ÊÓ

A population of college students is considered, and it is required to estimate the proportion of students capable of pursuing a statistics course by choosing a sample from a population of sufficient size.

To gain knowledge about the important characteristics of a large population of units, asmall group of unitsis selected from it and is called a sample.

As the sample does not contain all of the units, it produces some errors in the estimates of the population’s characteristics, calledsampling errors. To minimise sampling errors, anadequate sample size is to be considered.

Using the expression, the appropriate sample size is given as:

\(\begin{aligned}{c}\frac{{{{1.96}^2} \times 0.25}}{{{{0.03}^2}}} = \frac{{0.9604}}{{0.0009}}\\ = 1067.11\\ \approx 1067\end{aligned}\)

Thus, the appropriate sample size is equal to 1067.