Question

determine the necessary sample size.
what is the approximate sample size required to estimate the percentage of americans who have earned a college degree to within 2%, with 95% confidence?
recall: the worst case scenario would assume that p = 0.5
2401
3382
4145
1692
7156

Explanation:

Step1: Recall the formula for sample size in proportion

The formula for sample size \(n\) when estimating a proportion is \(n=\frac{z^{2}\cdot p(1 - p)}{E^{2}}\). For a 95% confidence interval, the critical value \(z\) (from the standard normal distribution) is \(z = 1.96\). The margin of error \(E=0.02\) and \(p = 0.5\) (worst - case scenario).

Step2: Substitute the values into the formula

Substitute \(z = 1.96\), \(p=0.5\), \(1 - p=0.5\) and \(E = 0.02\) into the formula:

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Answer:

2401