Suppose the porosity (in 96) of coal samples taken from the (now closed) Prince

Question

Suppose the porosity (in 96) of coal samples taken from the (now closed) Prince Mine at Point Acon, Nova Scotia was found to be normally distributed with -0.75 % a.) Compute a 90 % confidence interval for the true mean porosity of Prince Mine coal if a sample of 25 specimens had an average porosity of 4.6 %. (Give decimal answer to two places past decimal.) Lower bound: Upper bound Submit Answer Tries 0/5 b.) How large a sample size is necessary if the width of the 90 % CI is to be 0.35? (Give whole number answer.) Submit Answer Tries 0/5 c.) what sample size is necessary to estimate the true mean porosity to within 0.25 (ie with half width 0.25) with 95% confidence? (Give whole number answer.) Submit Answer Tries 0/5

Explanation / Answer

a)

for std error =std deviation/(n)1/2 =0.15

for 90% Ci ; z=1.6449

therefore lower bound =sample mean -z*Std error =4.35

upper bound=sample mean +z*Std error =4.85

b)

margin of error E=width/2 =0.35/2 =0.175

for 90% CI ; z=1.6449

therefore sample size =(z*std deviation/E)2 =~ 50

c)for margin of error E =0.25

for 95% CI ; z=1.96

therefore sample size =(z*std deviation/E)2 =~35

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