Question

correct answer
n = 3959
part: 1 / 2
part 2 of 2
if no estimate of the sample proportion is available, how large should the sample be?
n =

Explanation:

Step1: Recall the formula for sample size when no proportion estimate is available

When no estimate of the sample proportion \(p\) is available, we use \(p = 0.5\) (since \(p(1 - p)\) is maximized when \(p=0.5\)). The formula for sample size \(n\) in estimating a proportion is \(n=\frac{z^{2}_{\alpha/2}\times p(1 - p)}{E^{2}}\). Assuming a common confidence level (if not specified, often 95% confidence level is used). For a 95% confidence level, \(z_{\alpha/2}=1.96\) (from the standard normal distribution), and let's assume the margin of error \(E = 0.05\) (if not given, a common margin of error value is used for illustration purposes. If the margin of error was used in part 1, we should use the same value here). Substitute \(p = 0.5\), \(1-p=0.5\), \(z_{\alpha/2}=1.96\), and \(E = 0.05\) into the formula.

Step2: Calculate the sample size

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Since the sample size \(n\) must be an integer, we round up to \(n = 385\).

Answer:

\(n = 385\)