In a sample of seven cars, each car was tested for nitrogen-oxide emissions (in

Question

In a sample of seven cars, each car was tested for nitrogen-oxide emissions (in grams per mile) and the following results were obtained: 0.05, 0.16, 0.12, 0.14, 0.17, 0.06, 0.18. Assuming that this sample is representative of the cars in use, construct a 98% confidence interval estimate of the mean amount of nitrogen-oxide emissions for all cars. If the EPA requires that nitrogen-oxide emissions be less than 0.165 g/ mi, can we safely conclude that this requirement is being met? What is the confidence interval estimate of the mean amount of nitrogen-oxide emissions for all cars? Can we safely conclude that the requirement that nitrogen-oxide emissions be less than 0.165 g/mi is being met?

Explanation / Answer

1

=3.76/.88=4.2727,

=(3.1745/.88)=1.8993. The 98% confidence interval is +-(2.33)(/n)=(5.9454<4.2726<2.6). No, because the confidence interval does not contain 0.165g/ml and it is not possible that requirement is being met and mean is greater than .165g/ml.

x f fx f(xi-)2

1

.05 .05 .5355 2 .16 .32 .8264 3 .12 .36 .1944 4 .14 .56 .0104 5 .17 .85 .0899 6 .06 .36 .1790 7 .18 1.26 1.3389 Total .88 3.76 3.1745

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