Question

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

Answer 1

Option C) 1537

Step-by-step 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 =

`z_(stat)* (\sigma)/(√(n))`

`z_(critical)\text{ at}~\alpha_(0.05) = 1.96`

Putting values, we get,

`250 = 1.96* (5000)/(√(n))\\\\n = (1.96* (5000)/(250))^2\\\\n = 1536.64\\n \approx 1537`

Thus, the correct answer is

Option C) 1537