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How large a sample should be selected to provide a 95% confidence interval with a margin of error of 4? Assume that the population standard deviation is 40. Round your answer to next whole number.

Respuesta :

Answer:

The large sample size 'n' = 384.16

Step-by-step explanation:

Explanation:-

Given Margin of error = 4

Given Population standard deviation(σ)  = 40

The margin of error is determined by

[tex]M.E = Z_{0.05} \frac{S.D}{\sqrt{n} }[/tex]

[tex]4 = 1.96 \frac{40}{\sqrt{n} }[/tex]

Cross multiplication , we get

[tex]\sqrt{n} = \frac{40 X 1.96}{4}[/tex]

√ n = 19.6

squaring on both sides , we get

n = 384.16

Final answer:-

The large sample size 'n' = 384.16

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