Answer :
The sample size needed to calculate the average weekly salary for students at one college is 2698.
The term population mean, which is the average score of the population on a given variable, is represented by: μ = ( Σ Xi ) / N. The symbol 'μ' represents the population mean.
The (1 - α)% confidence interval for population mean (μ) is:
[tex]CI = x[/tex] ± [tex]\frac{z_{a} }{2}[/tex] * σ/[tex]\sqrt{n}[/tex]
The margin of error of a (1 - α)% confidence interval for population mean (μ) is:
[tex]MOE = \frac{z_{a} }{2}[/tex] * σ/[tex]\sqrt{n}[/tex]
The information provided is:
σ = $53
MOE = $2
The critical value of z for 95% confidence level is:
[tex]z_{\frac{a}{2} }[/tex] = [tex]z_{\frac{0.05}{2} }[/tex]
= [tex]z_{0.025}[/tex]
= 1.96
Compute the sample size as follows:
[tex]MOE = \frac{z_{a} }{2}[/tex] * σ/[tex]\sqrt{n}[/tex]
n = [([tex]z_{\frac{a}{2} }[/tex] * σ)/MOE]2
n = [tex](\frac{1.96*53}{2} )^{2}[/tex]
n = 2697.76
n ≅ 2698
Therefore,
The sample size needed to calculate the average weekly salary for students at one college is 2698.
To learn more about information visit Population mean :
brainly.com/question/28383845
#SPJ4
