In a sample of seven cars, each car was tested for nitrogen-oxide emissions (in
ID: 3429090 • Letter: I
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:
?
0.13,?
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.)
Explanation / Answer
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
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