Question

An automobile manufacturer has given its van a 31.2 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 performs over the manufacturer's MPG rating. After testing 210 vans, they found a mean MPG of 31.4 . Assume the population standard deviation is known to be 1.0 . Is there sufficient evidence at the 0.05 level to support the testing firm's claim?

Step 2 of 6:

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

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is ,

H₀ :   = 31.2

H_a :    31.2

Test statistic = z

= ( - ) / / n

= (31.4 - 31.2) / 1 / 210

= 2.90

Test statistic = 2.90

This is the right tailed test .

P(z > 2.90) = 0.0019

P-value = 0.0019

= 0.05

P-value <

Reject the null hypothesis .

There is sufficient evidence at the 0.05 level to support the testing firm's claim .