Question

Suppose you wish to estimate a population mean μ based on a sample of n observations. What sample size is required if you want your estimate to be within 2 of μ with probability equal to 0.95 if you know the population standard deviation σ is 12?

a. 139 b. 98 c. 127 d. 239 e. 196

Answer 1

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Solution

standard deviation =s =   =12

Margin of error = E = 2

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 ( Using z table ( see the 0.025 value in standard normal (z) table corresponding z value is 1.96 )

sample size = n = [Z/2* / E] 2

n = ( 1.96* 12/ 2 )2

n =139

Sample size = n =139