For the test of significance questions, clearly indicate each of the formal steps in the test...

For the test of significance questions, clearly indicate each of the formal steps in the test of significance.

Step 1: State the null and alternative hypothesis.
Step 2: Calculate the test statistic.
Step 3: Find the p-value.

Step 4: State your conclusion. (Do not just say “Reject H0” or “Do not reject H0”, state the conclusion in the context of the problem.)

Does using premium gas increase your miles per gallon? A study was conducted with nine vehicles that can run on regular gas to see if using premium gas will get better gas mileage. Each car in our sample was randomly filled first with either regular or premium gasoline, and the mileage for that tankful recorded. The mileage was recorded again for the same cars for a tankful of the other kind of gasoline. Is there evidence to suggest that using premium gas will increase your miles per gallon? (Use 10% significance level.)

Vehicle 1: Prem: 19 Reg: 20 Difference: -1

Vehicle 2: Prem: 35 Reg: 32 Difference: 3

Vehicle 3: Prem: 34 Reg: 33 Difference: 1

Vehicle 4: Prem: 18 Reg: 19 Difference: -1

Vehicle 5: Prem: 40 Reg: 37 Difference: 3

Vehicle 6: Prem: 26 Reg: 27 Difference: -1

Vehicle 7: Prem: 36 Reg: 33 Difference: 3

Vehicle 8: Prem: 28 Reg: 29 Difference: -1

Vehicle 9: Prem: 34 Reg: 31 Difference: 3

Mean: Prem: 30 Reg: 29 Difference: 1

St. Dev: Prem: 7.7 Reg: 6.1 Difference: 2.0

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