Question

Use the given information to find the minimum sample size required to estimate an unknown population mean μ.

Answer 1

Answer:

The number of business students that must be randomly selected to estimate the mean monthly earnings of business students at one college is 64.

Step-by-step explanation:

The (1 - α) % confidence interval for population mean is:

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

The margin of error for this interval is:

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

The information provided is:

σ = $569

MOE = $140

Confidence level = 95%

α = 5%

Compute the critical value of z for α = 5% as follows:

 $z_{\alpha/2}=z_{0.05/2}=z_{0.025}=1.96$

*Use a z-table.

Compute the sample size required as follows:

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

       $n=[\frac{z_{\alpha/2}\times \sigma}{MOE}]^{2}$

          $=[\frac{1.96\times 569}{140}]^{2}\\\\=63.457156\\\\\approx 64$

Thus, the number of business students that must be randomly selected to estimate the mean monthly earnings of business students at one college is 64.