Question

Suppose that the helium porosity (in percent) of carbon samples taken from any particular seam is normally distributed with a true standard deviation of 0.75.

a. Calculate a 95% confidence interval for the true average porosity of a seam, if the average porosity in 20 specimens of the seam was 4.85.
b. How large should a sample size be if the width of the 95% range has to be 0.40?
c. What sample size is needed to estimate true average porosity with 99% confidence for a maximum margin of error of 0.2?

Answer 1

Solution :

Given that,

a) Z/2 = Z0.025 = 1.96

Margin of error = E = Z/2 * ( /n)

= 1.96 * ( 0.75 /  20 )

= 0.33

At 95% confidence interval estimate of the population mean is,

  ± E   

= 4.85 ± 0.33

= ( 4.52, 5.18 )

b) margin of error = E = 0.40 / 2 = 0.20

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

n = [ 1.96 * 0.75 / 0.20]2

n = 54.02

Sample size = n = 55

c) margin of error = E = 0.20

Z/2 = Z0.005 = 2.576

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

n = [ 2.576 * 0.75 / 0.20]2

n = 93.31

Sample size = n = 94