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:
[tex]CI=\bar x\pm z_{\alpha/2}\ \frac{\sigma}{\sqrt{n}}[/tex]
The margin of error for this interval is:
[tex]MOE= z_{\alpha/2}\ \frac{\sigma}{\sqrt{n}}[/tex]
The information provided is:
σ = $569
MOE = $140
Confidence level = 95%
α = 5%
Compute the critical value of z for α = 5% as follows:
[tex]z_{\alpha/2}=z_{0.05/2}=z_{0.025}=1.96[/tex]
*Use a z-table.
Compute the sample size required as follows:
[tex]MOE= z_{\alpha/2}\ \frac{\sigma}{\sqrt{n}}[/tex]
[tex]n=[\frac{z_{\alpha/2}\times \sigma}{MOE}]^{2}[/tex]
[tex]=[\frac{1.96\times 569}{140}]^{2}\\\\=63.457156\\\\\approx 64[/tex]
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.
