Question

The level of nitrogen oxides (NOX) in the exhaust of cars of a particular model varies Normally with standard deviation σ =0.05 grams per mile (g/mi). A random sample of 12 cars of this particular model is taken and is found to have a mean NOX emission of = 0.298 g/mi. Government regulations call for NOX emissions no higher than 0.3 g/mi. Do the data provide evidence that this particular meets the government regulation? The test statistic for the appropriate null and alternative hypotheses is z = –0.139. z = 0.139. z = 0.298. z = 0.445.

Answer 1

z = -0.139

The data provide evidence that this particular meets the government regulation

Explanation:

To determine if the the data provide evidence that this particular meets the government regulation, we need to define a null and alternative hypothesis as:

H0: m = 0.3

H1: m > 0.3

where m is the population mean NOX emission.

Then, we need to find the appropriate statistic. So, taking into account that the model follows a Normal distribution with standard deviation equal to 0.05, the statistic is equal to:

`z=(x-m)/(s/√(n) )`

where x is the mean of the sample, m is 0.3 g/mi, s is the population standard deviation and n is the size of the sample.

Therefore, replacing x by 0.298, m by 0.3, s by 0.05 and n by 12, we get that the test statistic is:

`z=(0.298-0.3)/(0.05/√(12) )=-0.139`

Finally, we need to find the p-value using the normal distribution table as:

p-value = P(z > -0.139 ) = 0.4443

So, taking into account that the p-value is big value, we can conclude that we don't reject H0. It means that the data provide evidence that this particular meets the government regulation.