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 mpg were recorded each time the gas tank was filled, and the computer was then reset. In addition to the computer computing mpg, the driver also recorded the mpg 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 a random sample of 20 records. The driver wants to determine if these calculations are different. Assume the standard deviation of a difference to be ? = 3.0.

(a) State the appropriate H0 and Ha to test this suspicion.

H0: ? < 0 mpg; Ha: ? > 0 mpg

H0: ? > 0 mpg; Ha: ? < 0 mpg

    

H0: ? = 3 mpg; Ha: ? ? 3 mpg

H0: ? = 0 mpg; Ha: ? ? 0 mpg

H0: ? > 3 mpg; Ha: ? < 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 ? = 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.    

We conclude that ? ? 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 ? ? 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 ? ? 0 mpg; that is, we have strong evidence that the computer's reported fuel efficiency differs from the driver's computed values.

4.0 7.5 ?0.6 1.7 3.7 4.5 6.0 2.2 4.6 3.0 4.4 0.2 3.0 1.1 1.1 6.0 2.1 3.7 ?0.6 ?4.2

Explanation / Answer

(a) H0: ? = 0 mpg; Ha: ? ? 0 mpg

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(b)

The test statistic is

Z=(xbar-mu)/(s/vn)

=(2.67-0)/(3/sqrt(20))

=3.98

It is a two-tailed test.

So the p-value= 2*P(Z>3.98) =0 (from standard normal table)

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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.

count 20 mean 2.670 sample variance 7.410 sample standard deviation 2.722

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