Question

An automobile manufacturer claims that its van has a 40.3 miles/gallon (MPG) rating. An independent testing firm has been contracted to test the MPG for this van since it is believed that the van has an incorrect manufacturer's MPG rating. After testing 250 vans, they found a mean MPG of 39.9. Assume the standard deviation is known to be 2.4. A level of significance of 0.05 will be used. Find the value of the test statistic. Round your answer to 2 decimal places.

Answer 1

Answer:

The value of the test statistic is -2.64.

Step-by-step explanation:

The test statistic is:

$t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

In which X is the sample mean, $\mu$ is the expected(claimed) mean, $\sigma$ is the standard deviation and n is the size of the sample.

An automobile manufacturer claims that its van has a 40.3 miles/gallon (MPG) rating.

This means that $\mu = 40.3$

After testing 250 vans, they found a mean MPG of 39.9. Assume the standard deviation is known to be 2.4.

This means, respectively, that:

$n = 250, X = 39.9, \sigma = 2.4$

So

$t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

$t = \frac{39.9 - 40.3}{\frac{2.4}{\sqrt{250}}}$

$t = -2.64$

The value of the test statistic is -2.64.