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:

?

0.13,?

0.12,?

0.17,?

0.18,?

0.09,?

0.12,?

0.19.

?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?

?

______g/mi<?< _____g/mi?

(Round to three decimal places as needed.)

Solution

The sample size = 7

The sample mean=0.1428571

The sample standard deviation =0.03728909

Given a=1-0.98=0.02, t(0.01, df=n-1=7-1=6) =3.14 (from student t table)

So the lower bound is

xbar - t*s/vn =0.1428571 - 3.14*0.03728909/sqrt(7) =0.099

So the upper bound is

xbar + t*s/vn =0.1428571 + 3.14*0.03728909/sqrt(7) =0.187

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Since the interval includes 0.165, we can not conclude that nitrogen-oxide emissions be less than 0.165 g/mi