?Finding Sample Size Instead of using Table 7-2 for determining the sample size

Chapter 7, Problem 24

(choose chapter or problem)

Finding Sample Size Instead of using Table 7-2 for determining the sample size required

to estimate a population standard deviation \(\sigma\), the following formula can be used

\(n=\frac{1}{2}\left(\frac{z_{\alpha / 2}}{d}\right)^{2}\)

where \(z_{\alpha/2}\) corresponds to the confidence level and d is the decimal form of the percentage error. For example, to be 95% confident that s is within 15% of the value of \(\alpha\), use \(z_{\alpha/2} = 1.96\) and d = 0.15 to get a sample size of n = 86. Find the sample size required to estimate \(\sigma\) assuming that we want 98% confidence that s is within 15% of \(\sigma\).

Text Transcription:

sigma

n=1/2 (z_alpha/2/d)^2

z_alpha/2

z_alpha/2=1.96