Question

To estimate a population mean, the sample size needed to provide a margin of error of 3 or less with a 95% confidence when the population standard deviation equals 11 is
(Round your answer to the nearest integer.)

Answer 1

Answer:

The minimum sample needed to provide a margin of error of 3 or less is 52.

Step-by-step explanation:

The confidence interval for population mean (μ) is:

$\bar x\pm z_{\alpha /2}\frac{\sigma}{\sqrt{n}}$

The margin of error is:

$MOE= z_{\alpha /2}\frac{\sigma}{\sqrt{n}}$

Given:

MOE = 3

σ = 11

The critical value for 95% confidence interval is: $z_{\alpha /2}=1.96$

**Use the z-table for critical values.

Compute the sample size (n) as follows:

$MOE= z_{\alpha /2}\frac{\sigma}{\sqrt{n}}\\3=1.96\times \frac{11}{\sqrt{n}}\\n=(\frac{1.96\times11}{3} )^{2}\\=51.65\\\approx52$

Thus, the minimum sample needed to provide a margin of error of 3 or less is 52.