Question

An experiment reported in Popular Science compared fuel economies for two types of similarly equipped diesel mini-trucks. Let us suppose that 12 Volkswagen and 10 Toyota trucks were tested in 90 kilometer-per-hour steady paced trials. The sample of 12 Volkswa- gen trucks averaged 16 kilometers per liter with a standard deviation of 1.0 kilometer per liter and the sample of 10 Toyota trucks averaged 11 kilometers per liter with a standard deviation of 0.8 kilometer per liter. Assume that the distances per liter for the truck models are normally distributed. a. Let ? 2 1 denote the population variance of kilometers per liter for Volkswagen trucks. Construct a 95% confidence interval (C.I.) for ? 2 1 . b. Let ? 1 and ? 2 denote the population mean of kilometers per liter for Volkswagen and Toyota trucks, respectively. Construct a 95% C.I. for ? 1 ? ? 2 . Assume that ? 2 1 = ? 2 2 . c. Let ? 2 1 and ? 2 2 denote the population variance of kilometers per liter for Volkswagen and Toyota trucks, respectively. Construct a 95% C.I. for ? 2 1 /? 2 2 . Does the assumption that ? 2 1 = ? 2 2 seem reasonable? Explain

Answer 1

x1 = 16 ,s1 = 1 , n1 = 12
x2 = 11 , s2 = 0.8 , n2 = 10

z value at 95% = 1.96

CI = (x1 - x2) +/- z *sqrt(s1^2/n1 +s2^2/n2)
  
= ( 16-11) +/- 1.96 *sqrt(1^2/12 + 0.8^2/10)

= (4.2477 ,5.7523)