Oxides of nitrogen (called NOX for short) emitted by cars and trucks are importa

Question

Oxides of nitrogen (called NOX for short) emitted by cars and trucks are important contributors to air pollution. The amount of NOX emitted by a particular model varies from vehicle to vehicle. For one light truck model, NOX emissions vary with unknown mean mu and standard deviation sigma = .4 grams per mile. You test an SRS of 50 of these trucks and find the sample mean NOX level x = 8 grams per mile. Assume a normal distribution of samples has been observed in the past. Give a 90% confidence interval for the mean NOX level. Give a 95% confidence interval for the mean NOX level. Give a 99% confidence interval for the mean NOX level assuming the same sample mean value but with an SRS of 200 trucks.

Explanation / Answer

Given =0.4, xbar=8, n=50 (a) =0.1, Z(0.05)=1.645(check normal table) The 90% CI is xbar ± Z*/n --> 8 ± 1.645*8/sqrt(50) --> (6.14, 9.86) (b) =0.05, Z(0.025)=1.96(check normal table) The 95% CI is xbar ± Z*/n --> 8 ± 1.96*8/sqrt(50) --> (5.78, 10.22) (c) =0.01, Z(0.005)=2.58 (check normal table) , n=200 The 99% CI is xbar ± Z*/n --> 8 ± 2.58*8/sqrt(200) --> (6.54, 9.46)

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