The article “Quality of the Fire Clay Coal Bed,Southeastern Kentucky: (J. Howler

Question

The article “Quality of the Fire Clay Coal Bed,Southeastern Kentucky: (J. Howler, W. Andrews, et al., Journal ofCoal Quality, 1994:13-26) contains measurements on a samples ofcoal from several counties in Kentucky. In units of percentash, five samples from Knott County had an average aluminum dioxide(Al02) content of 32.17 and a standard deviation of 2.23. Sixsamples from Leslie County had an average Al02 content of 26.48 anda standard deviation o 2.02.   

Find a 98% confidence interval for the difference in Al02content between coal samples from the two counties.
The article “Quality of the Fire Clay Coal Bed,Southeastern Kentucky: (J. Howler, W. Andrews, et al., Journal ofCoal Quality, 1994:13-26) contains measurements on a samples ofcoal from several counties in Kentucky. In units of percentash, five samples from Knott County had an average aluminum dioxide(Al02) content of 32.17 and a standard deviation of 2.23. Sixsamples from Leslie County had an average Al02 content of 26.48 anda standard deviation o 2.02.   

Find a 98% confidence interval for the difference in Al02content between coal samples from the two counties.

Explanation / Answer

Given n1=5, xbar1=32.17, s1=2.23            n2=6,xbar2=26.48, s2=2.02 =0.02, Z(0.01)=2.326 (check normal table) The 98% CI is (xbar1-xbar2) ± Z*([s1^2/n2] + [s2^2/n2]) --> (32.17-26.48) ± 2.326*sqrt(2.23^2/5 + 2.02^2/6) --> ( 2.679, 8.07)

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