In a sample of seven cars was testaed for nitrogen-oxide emissions(in grams per
ID: 3378964 • Letter: I
Question
In a sample of seven cars was testaed for nitrogen-oxide emissions(in grams per miles) and the following results were obtained : 0.14, 0.13, 0.08, 0.07, 0.12, 0.17, 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 nitro-oxide emissions be less than 0.165g/mi can we safely conclude that this requirement is being met/
a) what is the confidence interval estimate of the mean amount of nitrogen- oxide emissions for all cars? ______g/mi,< U < __g/mi. round to 3 decimal places.
can we safely conclude that the requirement that nitrogen-oxide emissions be less than 0.165g/mi is being met?
Explanation / Answer
a)
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 = 0.128571429
t(alpha/2) = critical t for the confidence interval = 3.142668403
s = sample standard deviation = 0.043752551
n = sample size = 7
df = n - 1 = 6
Thus,
Lower bound = 0.076601404
Upper bound = 0.180541453
Thus, the confidence interval is
( 0.076601404 , 0.180541453 ) [ANSWER]
***********************
b)
NO, as 0.165 is inside this confidence interval.
[We could have concluded yes if the whole confidence interval is under 0.165, that is.]
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