Question

An automobile manufacturer claims that the new model gets an average of 30 miles per gallon on the highway, with a standard deviation of 5 miles. However, when a consumer group drove 100 cars on the highways. the group found the average mileage was 28.5 miles. what can the consumer group assert with 99% confidence? check your answer with the p-value test?

Answer 1

Solution:

Hypothesis are

H0 : = 30

H1 :     30

b)The test statistic z is given by

z =

= (28.5 - 30) / (5/100)

= -3.00

Now , observe that ,there is   sign in H1. So , the test is two tailed.

For two tailed test :

p value = 2 * P(Z < -z)

= 2 * P(Z < -3.00)

= 2 * 0.0013

= 0.0026

p value = 0.0026

Now , confidence level = c = 99% = 0.99

Significance level = = 1 - c = 1 - 0.99= 0.01

p value is less than

Reject H₀ at 0.01 level of significance .

Data provides the sufficient evidence to conclude that the average of new model is different from 30