Question

You want to obtain a sample to estimate a population mean. Based on previous evidence, you believe the population standard deviation is approximately σ = 39.9 σ=39.9. You would like to be 99% confident that your estimate is within 2 of the true population mean. How large of a sample size is required?

Answer 1

large of a sample size n = 2645

Step-by-step explanation:

Step-by-step explanation:-

The population standard deviation 'σ' = 39.9

Given data the estimate is within 2 of the true population mean so given the margin of error = 2

we know that margin of error is determined by

Margin of error =
`(z_(\alpha )S.D )/(√(n) )`

cross multiplication , we get

`√(n) = (2.578 X S.D)/(M.E)`

`√(n) = (2.578 X 39.9)/(2)= 51.4311`

squaring on both sides , we get

n = 2645.15

n = 2645

Conclusion:-

large of a sample size n = 2645