Question

How large a sample should be selected to provide a 95% confidence interval with a margin of error of 6? Assume that the population standard deviation is 40 . Round your answer to next whole number.

Answer 1

Solution :

Given that,

standard deviation = = 40

margin of error = E = 6

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96

Sample size = n = ((Z/2 * ) / E)2

= ((1.96 * 40) / 6)2

= 170.7377

Sample size = 170.737

[OR]

Answer:

= 40

Margin of error = 6  

Margin of error = (Z/2)(/)  

6 = (1.96)(40/)

6 = 78.4/

= 78.4/6

= 13.0666

n = 170.737

Thus, sample size n = 170 (approx.)

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