Question

An automobile manufacturer has given its car a 53.7 miles/gallon (MPG) rating. An independent testing firm has been contracted to test the actual MPG for this car since it is believed that the car performs under the manufacturer's MPG rating. After testing 200 cars, they found a mean MPG of 53.4. Assume the population variance is known to be 2.25. Is there sufficient evidence at the 0.02 level to support the testing firm's claim?

State the null and alternative hypotheses. ( i think it is H0: u=53.7 Ha: u<53.7)

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=200

Hypothesis

To test

Test statistics

It is one tailed test (left tailed)

P value

p value=P(Z<z)=P(Z<-1.89)=0.0294

Level of significance for the hypothesis test is

Decision

Rejection Rule:

Reject Ho if p value is less than significance level of 0.02

Here p value is greater than 0.02 hence we fail to reject the null hypothesis

There is no sufficient evidence at the 0.02 level to support the testing firm's claim