Question

4. [15] Suppose that you are an analyst for the non-profit auto safety and consumer advocacy organization known as Consumer for Auto Reliahility and Safety (CARS). You are investi- gating the average highway gas mileage for the new Toyota Prius. In this quest, you reuted and drove 20 new Toyota Prii (plural of Prius). e ta Tou began your investigation by finding a confidence interval. Assuming that all se remains unchanged, which of the following will yield a narrower confidence interval? (Circle one, no explanation needed.) Larger sample size Larger confidence level Both None (b) 12] Assuming that everything else remains the same, how would the standard eror of the mean change if you had rented 50 cars instead of 20? (Circle one, no explanation needed.) SMALLER LARGER NO CHANGE (c) [2] Let us assume that the 20 rental cars were random and their gas mileage are inde- pendent of each other. To check the validity of a confidence interval, what is the third condition would you need and how would you check this condition? Suppose that Toyota claims that the average highway gas mileage is at least 54 mpg for their new Prii. Use this information to answer parts (d) through (f) (d) [2] The null hypothesis to be tested here is Ho : u 2 54. What does u represent in context? (e) [3] The p-value of the test turns out to be 0.7472. Summarize the conclusion of this test in context at a= 0.05. (f) [4] Describe what a Type I error and Type II error would mean in this context. Type I error: Type II error:

Answer 1

d) Ho: 117,54 - The soung lighway gas mileage is represented by le We want to infer about the population mileage from the sample uileage. (e) pualue - 0.7472 7X (=0.05) This Ho is not rejected and the poplu mileage is accepted to be at least 54mpg of Type I error - P (Rejecting Ho] He is - ie. We reject to that the ideas true) is at least 54 mpg, but to is actually true true Type I error = P(Accepting to this sie wee accept to that milea i atleast 54 mpg but in reality wileage is less than 54 mpg