In a sample of seven cars was testaed for nitrogenoxide emis

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?

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 =    0.128571429          
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]

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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.]