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 0.76. (a) Compute a 95% Cl for the true average porosity of a certain seam if the average porosity for 18 specimens from the seam was 4.85. (Round your to two decimal places.) (b) Compute a 98% CI for true average porosity of another seam based on 15 specimens with a sample average porosity of 4.56. (Round your answers to two decimal places.) (c) How large a sample size is necessary if the width of the 95% interval is to be 0.36? (Round your answer up to the nearest whole number.) (d) What sample size is necessary to estimate true average porosity to within 0.25 with 99% confidence? (Round your answer up to the nearest whole numbers.) You may need to use the appropriate table in the Appendix of Tables to answer this question.

Explanation / Answer

z score =(X-mean)/std deviation

b)for std deviation of mean =std deviatrion/(n)1/2 =0.196

for 98% ; z=2.326

hence confidence interval =sample mean -/+z*std error =4.10 ; 5.02

c)sample szie =(z*std deviation/error)1/2 =~69

d)sample size =~62

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