Question.182 - The Case of the Different Gasoline Types A young, cost-conscious college student was concerned that he wasn’t getting the best value for his gasoline dollar. After all, didn’t the gasoline companies advertise that the higher grades of gasoline would lead to higher gas mileage? The student knew that the higher grades cost more but wondered if the higher cost would be offset by the higher number of miles per gallon. Always willing to save a buck, the student decided to run an experiment. The student found nine friends, all of whom owned cars, that were willing to be a part of the experiment. The student explained that the ten of them (including himself) would keep track of the next three times they filled up their gas tanks. On the first fill-up, they would all use Regular gasoline, on the second they would use Super gasoline and on the third they would use Ultra gasoline. At each fill-up the student conducting the research instructed his friends to compute the miles per gallon they had gotten from each of the brands of gas. At the end of the study, the student researcher collected the miles per gallon information from each student and plotted it into a table like the one seen below. Now, all he had to do was figure out how to appropriately analyze the data! Car 1 2 3 4 5 6 7 8 9 10 Regular 22 15 14 25 12 15 15 9 15 12 Super 22 15 14 25 12 15 15 9 15 15 Ultra 24 17 12 22 14 11 16 11 14 9 1. What is the hypothesis that the student is investigating? 2. What is the independent variable? What are the levels of the independent variable? 3. What is the dependent variable? 4. Which statistical test would he use to test his hypothesis? 5. For each of the sets of output below, what can you tell about the dependent variable? What decision would the student make? Case A: Gas Type N Mean Standard Standard Deviation Error of the Mean Regular 10 15.4 4.7422 1.4996 Super 10 15.7 4.5959 1.4533 Ultra 10 15.00 4.8762 1.5420 All Brands 30 15.37 4.5825 .8366 Sum of Degrees of Mean F value p value Squares Freedom Square MPG Between 2.467 2 1.233 .055 .947 Groups Within 606.500 27 22.463 Groups Total 608.967 29 Comparison Mean Difference Standard Error p value Regular to Super .30 2.120 .990 Regular to Ultra .40 2.120 .982 Super to Ultra .70 2.120 .947 Case B: Gas Type N Mean Standard Standard Deviation Error of the Mean Regular 10 20.40 4.4771 1.4158 Super 10 15.70 4.5959 1.4533 Ultra 10 15.00 4.8762 1.5420 All Brands 30 17.03 5.1090 .9328 Sum of Degrees of Mean F value p value Squares Freedom Square MPG Between 172.467 2 86.233 3.983 .030 Groups Within 584.500 27 21.648 Groups Total 756.967 29 Comparison Mean Difference Standard Error p value Regular to Super 4.7 2.081 .097 Regular to Ultra 5.4 2.081 .049 Super to Ultra .70 2.081 .945 Case C: Gas Type N Mean Standard Standard Deviation Error of the Mean Regular 10 20.4 4.4771 1.4158 Super 10 15.7 4.5959 1.4533 Ultra 10 45.0 6.2716 1.9833 All Brands 30 27.03 13.9913 2.5545 Sum of Degrees of Mean F value p value Squares Freedom Square MPG Between 4952.47 2 2476.2 92.282 .000 Groups Within 724.500 27 26.833 Groups Total 5676.97 29 Comparison Mean Difference Standard Error p value Regular to Super 4.7 2.317 .147 Regular to Ultra 24.6 2.317 .000 Super to Ultra 29.3 2.317 .000
Answer Below:
The xxxxxxxxxx that xxx student xx investigating xx whether xxx higher xxxxxx of xxxxxxxx leads xx higher xxx mileage xx advertised xx the xxxxxxxx companies xxxxxxxxxxx variable xx the xxxx of xxx gasoline xxxx Levels xx gasoline xxx Regular xxxxx and xxxxx Dependant xxxxxxxx is xxx mileage xxx gallon xxx student xxx use xxxxx sum xx squares xxxxx to xxxx its xxxxxxxxxx For xxxx A xxxxxxx p-value xx equal xx gt xxxxxxxxx there xx a xxxxxxxxxxx difference xx the xxx values xxxxx sum xx squares xxx p-value xx positive xxxxxxxxx there xx a xxxxxxx in xxx mileage xxx gallon xxx nbsp xxxxx the xxxxxxx will xxxxxx the xxxxxxxx companies xxxxx advertisement xxx -tailed xxxxxxx for xxxxxxx to xxxxx is xx The xxxxxxx p-value xxx Regular xx Ultra xx gt xxx -tailed xxxxxxx for xxxxx to xxxxx is xx Hence xxx student xxxx use xxx Regular xxxxx of xxx For xxxx B xxxxxxx p-value xx equal xx lt xxxxxxxxx there xx no xxxxxxxxxxx difference xx the xxx values xxxxx is xx increase xx the xxxxxxx per xxxxxx MPG xxxx Hence xxx student xxxx accept xxx gasoline xxxxxxxxx rsquo xxxxxxxxxxxxx The xxxxxxx p-value xxx Regular xx Super xx gt xxx -tailed xxxxxxx for xxxxxxx to xxxxx is xx The xxxxxxx p-value xxx Super xx Ultra xx gt xxxxx the xxxxxxx will xxx the xxxxx brand xx gas xxx case x -tailed xxxxxxx is xxxxx to xx therefore xxxxx is xx difference xx the xxx values xxxxx is xx increase xx the xxxxxxx per xxxxxx MPG xxxx Hence xxx student xxxx accept xxx gasoline xxxxxxxxx rsquo xxxxxxxxxxxxx The xxxxxxx p-value xxx Regular xx Super xx gt xxx -tailed xxxxxxx for xxxxxxx to xxxxx is xx The xxxxxxx p-value xxx Super xx Ultra xx lt xxxxx the xxxxxxx will xxx the xxxxx brand xx gasMore Articles From Maths
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