How large a sample should be selected to provide a 95% confidence interval with a margin of error of 9? Assume that the population standard deviation is 30

Business Apr 01, 2021

How large a sample should be selected to provide a 95% confidence interval with a margin of error of 9? Assume that the population standard deviation is 30. Round your answer to next whole number.

Expert Solution

Given that,

Standard deviation = σ = 30

Margin of error = E = 9

At 95% confidence level the z is ,

α = 1 - 95% = 1 - 0.95 = 0.05

α/ 2 = 0.05 / 2 = 0.025

Z_α/2 = Z_0.025 = 1.96

Sample Size = n = [Z_α/2* σ / E] ²

n = ( 1.96* 30 / 9 )²

n = 42.68 or 43

So, Sample Size is 43.

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