Answer:
The value of the test statistic is -2.64.
Step-by-step explanation:
The test statistic is:
[tex]t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the expected(claimed) mean, [tex]\sigma[/tex] 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 [tex]\mu = 40.3[/tex]
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:
[tex]n = 250, X = 39.9, \sigma = 2.4[/tex]
So
[tex]t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]t = \frac{39.9 - 40.3}{\frac{2.4}{\sqrt{250}}}[/tex]
[tex]t = -2.64[/tex]
The value of the test statistic is -2.64.
