2. Some people believe that higher-octane fuels result in better gas maleage for

Question

2. Some people believe that higher-octane fuels result in better gas maleage for their car. To test this claim, a researcher randomly selected 22 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, and the amer did not know which fuel was in the tank. Use the 0.05 level ofsupif cance. 87-octane 92-octane 234 256 243 214 5 286 214228 237 23 228 225 119 297 351 240

Explanation / Answer

The rationale of this test is to check whether there are any differences between the means of the two samples under consideration.

H0: 1 - 2 = 0 i.e. (1 = 2)

H1: 1 - 2 0 i.e. (1 2)

            

Assuming population variances are equal, we would have to calculate pooled-variance t-Test

Sp^2= (n1-1)S1^2+(n2-1)S2^2/(n1-1)+(n2-1)

         = (8-1)*49.89^2+(8-1)*66.08^2/7+7

         = 17425.5+30564.875/14

         = 3427.88

tSTAT=(X1-X2)-(µ1-µ2)/Sp^2(1/n1+1/n2)

       =(223.75-241.875)-0/3427.88(1/8+1/8)

       =-18.125/29.274

       =-0.6191

tCRIT is +/-2.1447 and hence the result does not lie in the rejection region and hence we cannot reject the null hypothesis. The P-Value is .545858. The result is not significant at p < .05. Hence, we conclude that higher octane fuel do not account for better gas mileage

87- Octane 92- Octane 234 237 256 238 243 228 214 225 115 119 286 297 214 351 228 240 223.75 241.875 Mean 49.89345792 66.07882198 SD

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