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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?

Respuesta :

Answer:

large of a sample size  n = 2645

Step-by-step explanation:

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 = [tex]\frac{z_{\alpha }S.D }{\sqrt{n} }[/tex]

cross multiplication , we get

                    [tex]\sqrt{n} = \frac{2.578 X S.D}{M.E}[/tex]

                    [tex]\sqrt{n} = \frac{2.578 X 39.9}{2}= 51.4311[/tex]

squaring on both sides , we get

                    n = 2645.15

                    n = 2645

Conclusion:-

large of a sample size  n = 2645

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