Question

An automobile manufacturer has given its van a 47.1 47.1 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 under the manufacturer's MPG rating. After testing 140 140 vans, they found a mean MPG of 46.9 46.9 . Assume the population variance is known to be 4.41 4.41 . Is there sufficient evidence at the 0.02 0.02 level to support the testing firm's claim? Step 4 of 6 : Find the P-value of the test statistic. Round your answer to four decimal places.

Answer 1

Solution :

Given that,

Population mean = = 47.1

Sample mean = = 46.9

Population standard deviation = = 2.1

Sample size = n = 140

Level of significance = = 0.02

This is a left (One) tailed test,

The null and alternative hypothesis is,  

Ho: 47.1

Ha: 47.1

The test statistics,

Z =( - )/ (/n)

= ( 46.9 - 47.1 ) / ( 2.1 / 140 )

= -1.13

P-value = P(Z < -1.13 )

= 0.1292

The p-value is p = 0.1292, and since p = 0.1292 > 0.02, it is concluded that the null hypothesis is not rejected.