Homework SourseIn 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:
0.12
0.06
0.16
0.18
0.19
0.11
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 0.165g divided by mig/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?
nothing
?(Round to three decimal places as? needed.)
Can we safely conclude that the requirement that? nitrogen-oxide emissions be less than 0.165
g divided by mig/mi is being? met?
A.?Yes, we can definitely conclude that the requirement is met for all cars.
B.?No, because the confidence interval does not contain 0.165 g/mi
C.?No, it is possible that the requirement is being? met, but it is also very possible that the mean is not less than 0.165 g/mi
D.Yes, because the confidence interval contains 0.165 g/mi
MUST SHOW WORK THANK YOU
Solution
Note that
Lower Bound = X - t(alpha/2) * s / sqrt(n)
Upper Bound = X + t(alpha/2) * s / sqrt(n)
where
alpha/2 = (1 - confidence level)/2 = 0.01
X = sample mean = 0.142857143
t(alpha/2) = critical t for the confidence interval = 3.142668403
s = sample standard deviation = 0.04785892
n = sample size = 7
df = n - 1 = 6
Thus,
Lower bound = 0.086009504
Upper bound = 0.199704782
Thus, the confidence interval is
( 0.086009504 , 0.199704782 ) [ANSWER]
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C.No, it is possible that the requirement is being met, but it is also very possible that the mean is not less than 0.165 g/mi [ANSWER, C]
This is because a part of the interval is less tha 0.165, but also a part of it is greater than 0.165.
