The researcher is interested in knowing whether cars running on regular or premi
ID: 3156291 • Letter: T
Question
The researcher is interested in knowing whether cars running on regular or premium gas have different gas mileage. In this study, we use 10 cars from a company fleet in which all the cars run on regular gas. Each car is filled first with either regular or premium gasoline, decide by coin toss, and the mileage for that tankful is recorded. Then the mileage is recorded again for the same cars for a tankful of the other kind of gasoline. The data are shown as follows. To test if these two type of gasoline provide significantly different mileage. Assume the significance level = 0.05.
The mean mileage of Regular is 23.10, Premium is 25.10
I need to find: T statistic, P value, 95% Confidence Interval for the mean difference, a statistical decision based on the P value and confidence interval and a conclusion.
Explanation / Answer
From information given, dbar=-2, sd=1.414, n=10 pairs
SE(dbar)=sd/sqrt n=1.414/sqrt 10=0.447
t9=(dbar-o)/SE(dbar)=-2-0/0.447=-4.47
p value at df=9 (n-1) and alpha=0.05 is 0.002
The 95% c.i=dbar+-t9,0.05SE(dbar)
=-2.0+-2.262*0.447
=-3.012 to -0.988
The p value is less than alpha=0.05, reject null hypothesis to conclude that two types of gasoline provides significantly different mileage. The confidence interval does not conatin 0, therefore, there is statistically significant difference in mileage og two gasoline.