7 4 Assume that the helium porosity in percentage of coal sa

7 #4

Assume that the helium porosity (in percentage) of coal samples taken from any particular seam is normally distributed with true standard deviation 0.77.

(c) How large a sample size is necessary if the width of the 95% interval is to be 0.31? (Round your answer up to the nearest whole number.)

(d) What sample size is necessary to estimate true average porosity to within 0.23 with 99% confidence? (Round your answer up to the nearest whole number.)

Solution

(a) E=0.31/2=0.155

Given a=1-0.95=0.05, Z(0.025) = 1.96 (from standard normal table)

So n=(Z*s/E)^2

=(1.96*0.77/0.155)^2

=94.80477

Take n=95

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(b)

Given a=1-0.99=0.01, Z(0.005) = 2.58 (from standard normal table)

So n=(Z*s/E)^2

=(2.58*0.77/0.23)^2

=74.60453

Take n=75