8) The 2008 Rambler Roadhog automobiles had mean gas mileage μ = 16.8 mpg, with standard deviation σ = 3.2 mpg. The Roadhog was completely redesigned for 2009 to meet federal mandates. A random sample of 1200 of the 2009 Roadhogs revealed mean gas mileage = 17.0 mpg. It is reasonable to assume that σ did not change in the redesign. Is there significant evidence that the mean gas mileage of the 2009 Roadhog is greater than 16.8 mph?

Set up appropriate null and alternative hypotheses, calculate the appropriate test statistic, find the P-value, and state your conclusion (using level of significance α = .01). 

 

Population mean (u) = 16.8

Population standard deviation (σ) = 3.2

Sample size (n) = 1200

Sample mean (x) = 17.0

Let Ho be the null hypothesis and H1 be the alternative hypothesis.

Ho : u = 16.8

H1 : u > 16.8

Test statistics is a z test and this is because sample size is greater than 30 (n=1200)

Test statistics is given below as

z = x - u/(σ/√n)

z = 17 - 16.8/(3.2/√1200)

z = 0.2/0.00577

z = 34.08

Test statistics is 34.08

The p value of this test statistics is denoted as z > 34.08 and it value is gotten from a standard normal distribution table.

From my table, p value is 0.0001

Decision rule

If p value is greater than 0.01, we accept the null hypothesis

If p is lesser than 0.01, we reject the null hypothesis

0.0001 is lesser than 0.01, hence we reject the null hypothesis.

In conclusion, there is enough evidence to prove that that the mean gas mileage of the 2009 Roadhog is greater than 16.8 mph