Computers in some vehicles calculate various quantities related to performance.

Question

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 =2.8=2.8 .

State the appropriate H0H0 and HaHa to test this suspicion. Carry out the test. Find the PP -value, and then interpret the result.

H0:=0H0:=0 versus Ha:>0Ha:>0

H0:=0H0:=0 versus Ha:<0Ha:<0

H0:=0H0:=0 versus Ha:0Ha:0

zz (±± 0.001) =

PP (±± 0.0001) =

Conclusion:

We don't have strong evidence that the computer's reported fuel efficiency differs from the driver's computed values.

We have evidence that the computer's reported fuel efficiency differs from the driver's computed values.

8.

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 =2.8=2.8 .

4.9 6.6 -0.6 1.7 3.7 4.5 7.9 2.2 4.9 3 4.4 0.2 3 1.1 1 5 2.2 3.7 -0.6 -4.2

State the appropriate H0H0 and HaHa to test this suspicion. Carry out the test. Find the PP -value, and then interpret the result.

H0:=0H0:=0 versus Ha:>0Ha:>0

H0:=0H0:=0 versus Ha:<0Ha:<0

H0:=0H0:=0 versus Ha:0Ha:0

zz (±± 0.001) =

PP (±± 0.0001) =

Conclusion:

We don't have strong evidence that the computer's reported fuel efficiency differs from the driver's computed values.

We have evidence that the computer's reported fuel efficiency differs from the driver's computed values.

Equation Editor

Explanation / Answer

H0:=0 versus Ha:0

mean value of above data Xbar =2.73

std error of ,mean =std deviaiton/(n)1/2 =2.8/(20)1/2 =0.6261

therefore test stat z =(X-mean)/std error =(2.73-0)/0.6261 =4.3603

p value =0.0000

We have evidence that the computer's reported fuel efficiency differs from the driver's computed values.

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