In 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: 0.09, 0.13, 0.18, 0.12, 0.07, 0.16, 0.05. 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/mi, can we safely conclude that this requirement is being met? Click here to view a t distribution table.

What is the confidence interval estimate of the mean amount of nitrogen-oxide emissions for all cars?

_____ g / mi < mu < _____ g / mi

Can we safely conclude that the requirement that nitrogen-oxide emissions be less than 0.165

g / mi is being met?

Yes, we can definitely conclude that the requirement is met for all cars.

Yes, because the confidence interval contains 0.165g / mi

No, because the confidence interval does not contain 0.165g / mi

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

Solution

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 =    0.114285714          
t(alpha/2) = critical t for the confidence interval =    3.142668403          
s = sample standard deviation =    0.047207748          
n = sample size =    7          
df = n - 1 =    6          
Thus,              
              
Lower bound =    0.058211549          
Upper bound =    0.17035988          
              
Thus, the confidence interval is              
              
(   0.058211549   ,   0.17035988   ) [ANSWER]

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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]

As we can see, the interval contains 0.165 (and even a part that is greater than that), so it is possible that it is not met.