Question

An automobile manufacturer has given its car a 31.131.1 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 over the manufacturer's MPG rating. After testing 110110 cars, they found a mean MPG of 31.331.3. Assume the population variance is known to be 3.613.61. Is there sufficient evidence at the 0.10.1 level to support the testing firm's claim?

Step 1 of 6:

State the null and alternative hypotheses.

Step 2 of 6:

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

Step 3 of 6:

Specify if the test is one-tailed or two-tailed.

Step 4 of 6:

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

Step 5 of 6:

Identify the level of significance for the hypothesis test.

Step 6 of 6:

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

Answer 1

Here, we have to use one sample z test for the population mean.

Step 1

The null and alternative hypotheses are given as below:

Null hypothesis: H₀: The average mileage of the cars is 31.1 miles/gallon.

Alternative hypothesis: H_a: The average mileage of the cards is more than 31.1 miles/gallon.

H₀: µ = 31.1 versus H_a: µ > 31.1

Step 2

The test statistic formula is given as below:

Z = (Xbar - µ)/[σ/sqrt(n)]

From given data, we have

µ = 31.1

Xbar = 31.3

σ = 1.9

n = 110

Z = (31.3 - 31.1)/[1.9/sqrt(110)]

Z = 1.1040

Step 3

This is an upper tailed (one tailed) test.

Step 4

P-value = 0.1348

(by using Z-table)

Step 5

α = 0.10

Step 6

P-value > α = 0.10

So, we do not reject the null hypothesis

There is not sufficient evidence to conclude that the average mileage of the cards is more than 31.1 miles/gallon.