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An economist is interested in studying the incomes of employees in a particular Silicon Valley firm. The population standard deviation is known to be $5000. What total sample size would the economist need to use for a 95% confidence interval if the width of the interval should not be more than $500:

A. 385
B.1536
C.1537
D. 384

Respuesta :

Answer:

Option C) 1537

Explanation:

We are given the following in the question:

Population standard deviation = $5000

95% confidence interval width = $500

Thus, margin of error = $250

Formula for margin of error =

[tex]z_{stat}\times \dfrac{\sigma}{\sqrt{n}}[/tex]

[tex]z_{critical}\text{ at}~\alpha_{0.05} = 1.96[/tex]

Putting values, we get,

[tex]250 = 1.96\times \dfrac{5000}{\sqrt{n}}\\\\n = (1.96\times \dfrac{5000}{250})^2\\\\n = 1536.64\\n \approx 1537[/tex]

Thus, the correct answer is

Option C) 1537