Question

30 Fuel efficiency. Computers in some vehicles calculate various quantities related to performance. One of these is the fuel efficiency, or gas mileage, usually expressed as miles per gallon (mpg). For one vehicle equipped in this way, the miles per gallon were recorded each time the gas tank was filled, and the computer was then reset. Here are the mpg values for a random sample of 20 of these records: MPG 41.5 43.2 50.7 44.6 36.6 48.4 37.3 46.4 34.2 46.8 45.0 39.2 48.0 43.2 37.3 43.5 47.7 42.2 44.3 43.3 Suppose that the standard deviation is known to be 0 - 3.5 mpg. (a) What is us, the standard deviation of x? (b) Examine the data for skewness and other signs of non-Normality. Show your plots and numerical summaries. Do you think it is reasonable to construct a confidence interval based on the Normal distribution? Explain your answer. (c) Give a 95% confidence interval for u, the mean miles per gallon for this vehicle. 16 More confidence interval mistakes and misunderstandings. Suppose that 100 randomly selected members of the Karaoke Channel were asked how much time they typically spend on the site during the week. The sample mean was found to be 3.8 hours. Assume that the population standard deviation is known to be o = 2.9. (a) Cary Oakey computes the 95% confidence interval for the average time on the site as 3.8 + 1.96(2.9/100). What is his mistake? (b) He corrects this mistake and then states that "95% of the members spend between 3.23 and 4.37 hours a week on the site." What is wrong with his interpretation of this interval? (c) The margin of error is slightly larger than half an hour. To reduce this to roughly 15 minutes, Cary says that the sample size needs to be doubled to 200. What is wrong with this statement?

Answer 1

(16) (a) Cary has deorded by loo. to showd dovede by too = 10 The Coreetton equation 15 3.8 + 1-96(3:0) recite (b) The Correct pnterpretaefton Ps that we are 95%. Confident that the population mean lees between 3-23 and 4.37 frowers to (c) Since sample size as conder a square root, therefore Bring the ME down by Ya, we need to meeltaply the Sample Sale by 4 temes ie we need 4 times the sample bize.