Question

Some people believe that​ higher-octane fuels result in better gas mileage for their car. To test this​ claim, a researcher randomly selected 11 individuals to participate in the study. Each participant received 10 gallons of gas and drove his car on a closed course. The number of miles driven until the car ran out of gas was recorded. A coin flip was used to determine whether the car was filled up with​ 87-octane or​ 92-octane first, and the driver did not know which fuel was in the tank. Complete parts​ (a) through​ (e). Click here to view the data, probability plots, and technology output. LOADING... Click here to view the table of critical values for the correlation coefficient. LOADING... ​(a) Why is it important that the matching be done by driver and​ car? A. How someone drives and the car they drive result in different fuel consumption. B. It allows each driver to determine which fuel is best for their car. C. It allows all of the trials to be done at the same time. D. It cuts the cost of doing the research. ​(b) Why is it important to conduct the study on a closed​ track? A. So that the researcher can watch the drivers B. So that each car travels the same distance C. So that all drivers and cars have similar driving conditions D. So that each car uses the same amount of gas ​(c) The normal probability plots and linear correlation coefficients for miles on​ 87-octane and miles on​ 92-octane are given. The correlation between 87 octane and the expected​ z-scores is 0.876. The correlation between 92 octane and the expected​ z-scores is 0.878. Are either of these variables normally​ distributed? A. ​No, neither variable is normally distributed. B. ​Yes, 92-octane is normally distributed. C. ​Yes, both variables are normally distributed. D. ​Yes, 87-octane is normally distributed. ​(d) The differences are computed as​ 92-octane minus​ 87-octane. The normal probability plot of the differences is shown. The correlation between the differenced data and the expected​ z-scores is 0.951. Is there reason to believe that the differences are normally​ distributed? ▼ No, Yes, since the ▼ correlation coefficient slope of the line is ▼ greater than less than equal to ▼ 0. the critical value. 0.5. 1. ​(e) The researchers used a statistical software package to determine whether the mileage from​ 92-octane is greater than the mileage from​ 87-octane. What do you conclude at alphaequals0.05​? ​Why? Begin by writing the hypotheses. Upper H 0​: The difference in mileage for​ 92-octane and​ 87-octane ▼ is greater than is different from equals is less than zero. Upper H 1​: The difference in mileage for​ 92-octane and​ 87-octane ▼ is less than equals is different from is greater than zero. The test statistic is nothing. ​(Do not​ round.) The​ P-value is nothing. ​(Do not​ round.) ​Therefore, there ▼ is is not sufficient evidence that the mileage from​ 92-octane ▼ is the same as is different from is greater than is less than the mileage from​ 87-octane. Click to select your answer(s).

Answer 1

a)

How someone drives and the car they drive result in different fuel consumption

b)

So that all drivers and cars have similar driving conditions

c)

Histogram for 87 octance

Histogram for 92 octance

​No, neither variable is normally distributed.

d) Yes, since the slope of the line correlation coefficient is less than the critical value of 0.05.

e)

H0​: The difference in mileage for​ 92-octane and​ 87-octane equals zero. Upper

H1​: The difference in mileage for​ 92-octane and​ 87-octane is greater than zero.

The test statistic is 1.02228801640586 ​(Do not​ round.) The​ P-value is .165389 ​(Do not​ round.) ​Therefore, there is not sufficient evidence that the mileage from​ 92-octane is greater than from the mileage from​ 87-octane.