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.

A

The  test statistics is  

B

The  Null and  Alternative hypothesis are

        and  

Step-by-step explanation:

From the question we are told that

    The population mean is  

    The sample size is  

     The  sample mean is  

      The sample  standard deviation is  

      The level of significance is  

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  

The alternative Hypothesis  is  

The test statistics can be mathematically evaluated as  

substituting values

arrange the equations with like terms in columns.

analyze the coefficients of x or y.

add the equations and solve for the remaining variable.

substitute the value into either equation and solve.

check the solution.

step-by-step explanation: