In a sample of seven cars each car was tested for nitrogenox

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?

Solution

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