Question

find the margin of error for a 95% confidence interval for estimating the population mean when the sample standard deviation equals 100, with a sample size of (i) 400 and (ii) 1600 what is the effect of the sample size? (i) find the margin of error for a 95% confidence interval for estimating the population mean when the sample standard deviation equals 100 with a sample size of 400. (round to two decimal places as needed)

Explanation:

Step1: Recall the formula for margin of error

The formula for margin of error \(E = z_{\alpha/2}\frac{s}{\sqrt{n}}\). For a 95% confidence interval, \(z_{\alpha/2}=1.96\), \(s = 100\).

Step2: Substitute values for \(n = 400\)

When \(n = 400\), we have \(E=1.96\times\frac{100}{\sqrt{400}}\). First, \(\sqrt{400}=20\). Then \(E = 1.96\times\frac{100}{20}\).

$$E=1.96\times5=9.80$$

Answer:

\(9.80\)