Question

An automobile manufacturer has given its van a 30.7miles/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 performs over the manufacturer's MPG rating. After testing 110 vans, they found a mean MPG of 30.9. Assume the population variance is known to be 3.61. Is there sufficient evidence at the 0.05 level to support the testing firm's claim?

State the null and alternative hypotheses. ( i think it is Ho: u=30.7 . Ha: u>30.7)

Find the value of the test statistic. Round your answer to two decimal places.

Specify if the test is one-tailed or two-tailed. (i think 1 tailed)

Find the P-value of the test statistic. Round your answer to four decimal places.

Identify the level of significance for the hypothesis test.

Make the decision to reject or fail to reject the null hypothesis.

Answer 1

n=110

Hypothesis

To test

Test statistics

This is one tailed test (Right tailed)

P value

p value=P(Z>0.58)=0.281

Level of significance for the hypothesis test is

Decision

Rejection Rule:
Reject the null hypothesis if p value is less than significance level of 0.05

Here p value is greater than 0.05 hence we fail to reject the null hypothesis.

There is no sufficient evidence at the 0.05 level to support the testing firm's claim