Question

2) In order to develop a confidence interval for the average miles per gallon (MPG) for a brand of hybrid car, a simple random sample of 97 cars is selected from the population of 10,000 cars manufactured. The 97 cars had a sample mean MPG of 51.9 MPG and a sample standard deviation of 4.5 MPG. (6 points) a) Compute a 99% confidence interval for the average miles per gallon (MPG) for this brand of car. b) Imagine that an advertisement claims a population average MPG of 52.85 miles per gallon for this brand of car. Based on your work above, state if you would challenge (reject) this claim or fail to reject this claim. (circle one) Reject the claim of u 52.85 miles per gallon Do not reject the claim of u 52.85 miles per gallon c) Carefully state why you decided to reject or to not reject the claim of u per gallon. Reference your interval for full credit. 52.85 miles

Answer 1

a) Here,

51.9, s4.5, n = 97

a 99% confidence interval for the average miles per gallon (MPG) for this brand of car

to.005,n-1 n (a to.005,n-1, r

4.5 4.5 to.005,96, 51.9+ V97 (51.9 *to.005,96 /97

4.5 4.5 2.62802, 51.9+072.62802) V97 (51.9

(50.6992, 53.1008

b)- c) Since 52.85 lies in the confidence interval, so we fail to reject the claim of miles per gallon at (1 - 0.99) = 0.01 level of significance.

52.85