I need help with this problem. Does octane matter? Some people believe that higher octane fuels result in better gas mileage for theircars. To test this claim, a researcher randomly selected 11 individuals (and their cars) to participate in thestudy. Each individual was given 10 gallons of 87-octane fuel and 10 gallons of 92-octane fuel. The numberof miles each driver was able to drive until they ran out of gas with each type of fuel is recorded below.DriverMiles on 87-OctaneMiles on 92-Octane1H₁: H-3422-2 -1 02+1Critical value(s):3473 282c. Find the test statistic.d. Find the p-value.4280b. Find the critical value and sketch the rejection region.Sketch of Rejection Region:+2 35045506Can the researcher conclude that higher octane fuels result in better gas mileage? Use the a = 0.08 level.a. State the null and alternative hypotheses.Ho: μ ν7413 494 274 298 461 287 233 247 464 229 488299 2348249 4419(If there are two critical values, list both values separated by a comma)+++++-3 -2 -1 0 1 2 3 -3 -2 -110234+0 1114742 3

Does octane matter? Some people believe that higher octane fuels result in better gas mileage for their cars. To test this claim, a researcher randomly selected 11 individuals (and their cars) to participate in the study. Each individual was given 10 gallons of 87-octane fuel and 10 gallons of 92-octane fuel. The number of miles each driver was able to drive until they ran out of gas with each type of fuel is recorded below. Driver Miles on 87- Octane Miles on 92- Octane 1 422 2 473 413 494 274 298 Critical value(s): 3 282 c. Find the test statistic. 4 = V d. Find the p-value. 280 0 5 OF 0 455 b. Find the critical value and sketch the rejection region. Sketch of Rejection Region: 6 299 461 287 7 234 Can the researcher conclude that higher octane fuels result in better gas mileage? Use the a = 0.08 level. a. State the null and alternative hypotheses. Ho: μ ν H₁: V 8 OF 9 249 441 (If there are two critical values, list both values separated by a comma) 10 मुंगेर समोर आयो -3 -2 -1 0 1 2 3 -3 -2 -1 0 1 2 3 -3 -2 -1 0 1 2 3 O 233 247 464 229 488 11 234 474