Question

3. -/3 points MINTROSTAT9 6.E.075. My Notes Ask Your Teacher v 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. In addition to the computer's calculations of miles per gallon, the driver also recorded the miles per gallon by dividing the miles driven by the number of gallons at each fill-up. The following data are the differences between the computer's and the driver's calculations for that random sample of 20 records. The driver wants to determine if these calculations are different. Assume that the standard deviation of a difference is o = 3.0. 4.9 -0.6 3.0 -4.2 6.0 7.5 -0.6 1.8 3.7 4.5 7.0 2.2 4.4 0.5 3.0 1.2 1.2 5.0 2.1 3.6 (a) State the appropriate Ho and Ma to test this suspicion Ho: Al> 0 mpg; Hail < 0 mpg Ho: y = 0 mpg; Ha: 0 mpg HO: > 3 mpg; Ha: 1 < 3 mpg Ho: 4 < 0 mpg; Haile > 0 mpg O Ho: d = 3 mpg; Ha: 11 # 3 mpg (b) Carry out the test. Give the P-value. (Round your answer to four decimal places.) Interpret the result in plain language. We conclude that u = 0 mpg; that is, we have strong evidence that the computer's reported fuel efficiency differs from the driver's computed values. We conclude that u #0 mpg; that is, we have strong evidence that the computer's reported fuel efficiency does not differ from the driver's computed values. We conclude that I # 3 mpg; that is, we have strong evidence that the computer's reported fuel efficiency differs from the driver's computed values. We conclude that u = 3 mpg; that is, we have strong evidence that the computer's reported fuel efficiency does not differ from the driver's computed values. We conclude that # 0 mpg; that is, we have strong evidence that the computer's reported fuel efficiency differs from the driver's computed values.

Answer 1

solution Here Ho U=0 vs Hill to from the given data n=20, d=2.81, 0=3 Test statutic z= dm = 2.8 1 = 1.19 P-value = 2p(27.4.19)=0.0000] here P-value Loos, so, we reject to. so, we conclude that u to mpg . - That is we have strong evidence that the computer's - reported field fuel efficiency differ from the driver's computed Values. 2 Here Horl=0.66 vs Hill 30.66 b) test statistic z =1.72 P_value =P(2>1.72) = 1-P(ZL1-72) =1-0.9573=0.0427 20.05 At 5%, z-value = 1.645 here cal z=1.72 1.6us, so, reject Ho, it is significant- YES, because z> 16u5 and p 20.05 crit 2 At ly, z-value = 2.326 P_value =0.0027>0.01 herez -Value = 1.72 22-326 No, this is not significant No, because z 22.326 and P >0.01