In a sample of seven? cars, each car was tested for? nitrogen-oxide emissions? (
ID: 3128241 • 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: 0.16?,0.09?,0.18?,0.12?,0.08?,0.17?,0.09.
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 0.165g/mi is being? met?
A. ?No, it is possible that the requirement is being? met, but it is also very possible that the mean is not less than 0.165g /mi.
B. ?Yes, we can definitely conclude that the requirement is met for all cars.
C.? No, because the confidence interval does not contain 0.165g /mi.
D. Yes, because the confidence interval contains 0.165g/mi.
Explanation / Answer
In a sample of seven cars, each car was tested for nitrogen-oxide emissions (in grams per mile) and the following results were obtained: 0.16,0.09,0.18,0.12,0.08,0.17,0.09.
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.) Could you please show me how you got the answer for this part of the problem; thanks.
First calculate mean and sd.
emission
n
7
mean
0.1271
sample standard deviation
0.0423
sample variance
0.0018
n=7
98% Table value t at 7-1 = 6 DF =3.1427
CI = ar x pm t* rac {s}{sqrt{n}}
= 0.1271 pm 3.1427* rac {0.0423}{sqrt{7}}
=(0.077, 0.177)
98% CI = (0.077, 0.177)
Can we safely conclude that the requirement that nitrogen-oxide emissions be less than 0.165g/mi is being met?
A. No, it is possible that the requirement is being met, but it is also very possible that the mean is not less than 0.165g /mi.
B. Yes, we can definitely conclude that the requirement is met for all cars.
C. No, because the confidence interval does not contain 0.165g /mi.
D. Yes, because the confidence interval contains 0.165g/mi.
emission
n
7
mean
0.1271
sample standard deviation
0.0423
sample variance
0.0018
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