Assume that the helium porosity (in percentage) of coal samples taken from any p

Question

Assume that the helium porosity (in percentage) of coal samples taken from any particular seam is normally distributed with true standard deviation 0.78. (a) Compute a 95% CI for the true average porosity of a certain seam if the average porosity for 18 specimens from the seam was 4.85 (b) Compute a 98% CI for true average porosity of another seam based on 17 specimens with a sample average porosity of 4.56. How large a sample size is necessary if the width of the 95% interval is to be 0.35? What sample size is necessary to estimate true average porosity to within 0.18 with 99% confidence?

Explanation / Answer

a)for std error =std deviation/(n)1/2 =0.1838

for 95% CI, z=1.96

hence confidence interval =sample mean -/+ z*Std error =4.48 ; 5.22

b)for std error =0.189

for 98% CI, z=2.326

hence  confidence interval =sample mean -/+ z*Std error = 4.12 ; 5.00

c)for 95% CI; z=1.96

margin of error E =0.35

sample size n=(z*std deviation/E)2 =~20

d)for 99% CI; z=2.5758

margin of error E =0.18

sample size =~125

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