For Chapter 2 through Chapter 14, the Cumulative Review Exercises include topics from preceding chapters. For this chapter, we present a few calculator warm-up exercises, with expressions similar to those found throughout this book. Use your calculator to find the indicated values.

Determining Sample Size The given expression is used to determine the size of the sample necessary to estimate the proportion of college students who have the profound wisdom to take a statistics course. Find the value and round the result to the nearest whole number.

\(\frac{{{{1.96}^2} \times 0.25}}{{{{0.03}^2}}}\)

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.