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 σ = 3.0.

6.0 7.5 −0.6 1.5 3.7 4.5 6.0 2.2 4.8 3.0

4.4 0.3 3.0 1.1 1.1 5.0 2.1 3.7 −0.6 −4.2

(a) State the appropriate

H₀  and H_a  to test this suspicion.

CORRECT: H₀: μ = 0 mpg;    H_a: μ ≠ 0 mpg

(b) Carry out the test. Give the P-value. (Round your answer to four decimal places.)

Answer 1

Let D_i represents the values of this sample and be the population mean.

Average of the sample, = 3.524

n = 20

A.

So to check out if the calculations are different there should not be any difference between the values and so we should test the following hypothesis.

H₀: = 0

H₁: 0

B.

Since   = 3

Assumption: Population is normally distributed.

Test statistic, z = (-)//

= (3.524-0)*/3

= 5.253

p-value = 1.5199*10^-7 < 0.05 (signifcance level) i.e. we can reject the null hypothesis and thus can say that calculations are different.

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