In a sample of seven cars, each car was tested for nitrogen oxide emissions in g
ID: 3023336 • Letter: I
Question
In a sample of seven cars, each car was tested for nitrogen oxide emissions in grams per mile and the folo ng results were obtained 0.18, 13, 0.1 0 15 0.09, 0.09, 0.16 Assuming hat his sample is representative of the cars in use, construct a 98% confidence interval estimate o he mean amount of nitrogen oxide emissions or all cars. If the EPA requires that nitrogen oxide emissions be less than 0.165 g / mi can we sate conclude that this requirement is being met? Click here to view a t distribution table. Click here to view page 1 of the standard normal distribution table. er iew page 2 of t tandard normal distribution table What is the confidence interval estimate of the mean amount of nitrogen-oxide emissions for all cars? Round to three decimal places as needed.) Can we safely conclude that the requirement that nitrogen-oxide emissions be less than 0.165 g/mi is being met? O A. O B. ° C. 0 D. Yes, we can definitely conclude that the requirement is met for all cars. No, because the confidence interval does not contain 0 165 g/ml. 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. Yes, because the confidence interval contains 0.165 g / mi.Explanation / Answer
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 = 0.13
t(alpha/2) = critical t for the confidence interval = 3.142668403
s = sample standard deviation = 0.035118846
n = sample size = 7
df = n - 1 = 6
Thus,
Lower bound = 0.088285238
Upper bound = 0.171714762
Thus, the confidence interval is
( 0.088285238 , 0.171714762 ) [ANSWER]
***********************
As we can see, 0.165 is inside this interval. Hence,
OPTION 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]
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