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 :s = 3.0 3.0 7.5-0.6 1.5 3.7 4.5 6.0 2.24.73.0 4.4 0.5 3.0 1.2 1.2 5.0 2.13.8-0.6 -4.2 (a) State the appropriate Ho and Ha to test this suspicion Ho: > 0 mpg; 0H0: > 3 mpg; Ho:

Explanation / Answer

using stat disk,

the output as follows

Null hypothesis

H0: mu = 3
Alternative Hypothesis:
Ha: mu not equal 3

Test Statistic, ChiSq: 14.7099
Lower Critical ChiSq: 8.906501
Upper Critical ChiSq: 32.85229
P-Value: 0.5183

95% Confidence interval:
2.007446 < SD < 3.855433
4.02984 < Var < 14.86437

p value > alpha

failed to reject null hypothesis.

accept that mu not equal to 3

we conclude that mu not eual to 3 ,that is we have strong evidence that the conputers reported fuel efficiency differe from the drivers computed value

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