Question

An automobile manufacturer has given its van a 47.2 miles/gallon (MPG) rating. An independent testing firm has been contracted to test the actual 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 47.0. Assume the population standard deviation is known to be 1.9. A level of significance of 0.02 will be used.
A. Find the value of the test statistic.
B. State the null and alternative hypotheses.

Answer 1

Answer:

A

The  test statistics is  $t = -1.7$

B

The  Null and  Alternative hypothesis are

      $H_o : \mu = 47.2$   and  $H_a : \mu \ne 47.2$

Step-by-step explanation:

From the question we are told that

    The population mean is  $\mu = 47.2 miles/gallon(MPG)$

    The sample size is  $n = 250 \ van$

     The  sample mean is  $\= x = 47.0$

      The sample  standard deviation is  $\sigma = 1.9$

      The level of significance is  $\alpha = 0.02$

Given that the value which the manufacturer gave the automobile is  47.2 and  it is believed that this is not correct, then  

The  Null Hypothesis is  

        $H_o : \mu = 47.2$

The alternative Hypothesis  is  

        $H_a : \mu \ne 47.2$

The test statistics can be mathematically evaluated as  

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

substituting values

        $t = \frac{\= 47- 47.2}{\frac{1.9 }{\sqrt{250} } }$

       $t = -1.7$