Question

A 95% confidence interval for a population mean was reported to be 148.79 to 155.21. If σ = 15, what sample size was used in this study? (Round your answer to the nearest integer.)

Answer 1

Solution :

given that

Lower confidence interval = 148.79

Upper confidence interval = 155.21

  = (Lower confidence interval + Upper confidence interval ) / 2

= ( 148.79+155.21 ) / 2

Sample mean = =152

Margin of error = E = Upper confidence interval -

= 155.21-152

Margin of error = E  =3.21

standard deviation =   =15

Margin of error = E = 3.21

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96

sample size = n = [Z_/2* / E] ²

n = ( 1.96* 15 / 3.21 )²

n =84