Question

An automobile manufacturer claims that their leading car averages 36 mpg in the city with a population standard deviation of 6 mpg for city driving. suppose a city police department purchases 64 cars from this auto manufacturer. If these cars were drivin exclusively under city conditions and averaged 34 mpg, can one argue that the manufacturer's claim is incorrect at a = 5%?

Answer 1

Solution:

H0 : = 36

Ha :   36

Test statistic z = = [34 - 36]/[6/64] = -2.67

Test statistic z = -2.67

Now , observe that sign in Ha

So , It is right tailed test

p value = P(Z < -z) + P(Z > +z) = P(Z < -2.67) + P(Z > +2.67) = 0.0038+0.0038 = 0.0076

Given alpha level is 5% i.e. 0.05

p value is less than 0.05

So ,

Reject H₀

There is sufficient evidence to reject the manufacturer's claim.