Question

Suppose your boss wants you to obtain a sample to estimate a population mean. Based on previous analyses, you estimate that 49 is the approximate value of the population standard deviation. You would like to be 99% confident that your estimate is within 38 of the true population mean. What is the minimum sample size required

Answer 1

the minimum sample size n = 11.03

Explanation:

Given that:

approximate value of the population standard deviation
`\sigma` = 49

level of significance ∝ = 0.01

population mean = 38

the minimum sample size n = ?

The minimum sample size required can be determined by calculating the margin of error which can be re[resented by the equation ;

Margin of error =
`Z_( \alpha /2)} * (\sigma)/(√(n))`

`38 = (2.576 * 49)/(√(n))`

`√(n) = (2.576 * 49)/(38)`

`√(n) = (126.224)/(38)`

`√(n) = 3.321684211`

`n= (3.321684211)^2`

n ≅ 11.03

Thus; the minimum sample size n = 11.03