Question

Sample Size for Proportion Find the sample size required to estimate the percentage of college students who take a statistics course. Assume that we want 95% confidence that the proportion from the sample is within four percentage points of the true population percentage.

Short answer

The sample size required to estimate the proportion of college students who take a statistics course is equal to 601

Step-by-step solution

Given information

It is given that the confidence level is equal to 95%. The sample proportion should be within four percentage points of the true population percentage.

It is needed to determine the sample size required to estimate the proportion of college students who take a statistics course.

Determination of sample size

The following formula is used to determine the sample size to estimate the proportion of college students who take a statistics course:

$n=\frac{{\left[z_{\frac{\alpha }{2}}\right]}^{2}0.25}{E^2}$

Here, it is given that the confidence level is equal to 95%. Thus, the level of significance will be equal to 0.05.

The corresponding value of $z_{\frac{\alpha }{2}}$ will be equal to 1.96.

It is given that the sample proportion should be within four percentage points of the true population proportion.

Thus, the margin of error (E) is equal to 0.04.

The following value of the sample size is obtained by substituting these values:

$$\begin{gathered} n=\frac{{\left[z_{\frac{\alpha }{2}}\right]}^{2}0.25}{E^2} \\ =\frac{{\left(1.96\right)}^{2}0.25}{{0.04}^2} \\ =600.25 \\ \approx 601 \end{gathered}$$

Thus, the sample size required to estimate the proportion of college students who take a statistics course when the confidence level is equal to 95% and the margin of error is equal to 0.04 is equal to 601.