Question

3. Sample size for estimating a population mean Aa Aa The online clothing retailer e-Parel is conducting a study to estimate the average size of the orders placed by visitors to its website The project manager desires a $40 maximal margin of error at 90% confidence The population standard deviation is unknown, but a preliminary study of a random sample of 55 orders placed at the firm's website provided s $175. use the Distributions tool to help you answer the questions that follow t Distibution Degrees of Freedom 50 SOOD 500 1.0 2.0 3.0 6 479 The critical value for a 90% confidence interval of the population mean is in order to satisfy the requirement of a s4o maximal margin of error, a sample size no smaller than is needed Continue withour saving ce Ter of UseBrvacy NoticeSecurity Notce

Answer 1

The critical value for a 90% confidence interval of the population mean is

$t_{critical}=t_{\frac{1-0.9}{2},n-1}=t_{0.05,54} = 1.67356$

Given,

Margin of error = 40

$\Rightarrow \frac{s}{\sqrt{n}}*t_{critical} = 40$

$\Rightarrow \frac{175}{\sqrt{n}}*1.67356 = 40$

$\Rightarrow \sqrt{n}=\frac{175}{40}*1.67356$

$\Rightarrow \sqrt{n}=7.32182$

$\Rightarrow n=7.32182^2 = 53.6091$

$\Rightarrow n \approx 54$ (ans)