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: 0.08, 0.16, 0.07, 0.19, 0.06, 0.14, 0.07.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 0.165 g? mi, can we safely 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. Click here to view page 2 of the standard normal distribution table. What is the confidence interval estimate of the mean amount of nitrogen-oxide emissions for all cars? g/mi

Solution

Sample given has total = 0.77

no of entries =7

Mean =0.11

Var(X) = 0.00234

std error = sigma/rt7 = 0.01828

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98% confidence level is Mean + or - z 0.49(se)

=0.11-2.33(0.01828) ,0.11+2.33(0.01828)

= (0.11-0.0426, 0.11+0.0426)

=(0.0067,0.1526)

0.007< mu < 0.153

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As the confidence interval is wholly below 0.165 we safely conclude that the requirement is being met.