You want to be $95 \%$ confident that the sample variance is within $40 \%$ of the population variance. Find the appropriate minimum sample size.
A) 57
B) 14
C) 11
D) 224

Question

Quizplus · Accepted Answer

The sample size is given by the formula:$$n = \frac{z^2 \sigma^2}{E^2}$$where $z$ is the z-score for the desired confidence level, $\sigma^2$ is the population variance, and $E$ is the margin of error.In this case, we have:$z = 1.96$ (for a 95% confidence level)$\sigma^2 = 1$ (since the population variance is unknown)$E = 0.4 \sigma^2 = 0.4$Plugging these values into the formula, we get:$$n = \frac{1.96^2 \cdot 1}{0.4^2} = 57.64$$Rounding up to the nearest whole number, we get a minimum sample size of 58.

You Want to Be 95%95 \%95% Confident That the Sample Variance Is Within

You Want to Be $95 \%$ Confident That the Sample Variance Is Within