Question

Some people believe that different octane gasoline result in different miles per gallon in a vehicle. The following data is a sample of 11 people which were asked to drive their car only using 10 gallons of gas and record their mileage for each 87 Octane and 92 Octane.

Person	Miles with 87 Octane	Miles with 92 Octane
1	234	237
2	257	238
3	243	229
4	215	224
5	114	119
6	287	297
7	315	351
8	229	241
9	192	186
10	204	209
11	547	562

Do the data support that different octanes produce different miles per gallon at the α=0.02α=0.02 level of significance? Note: A normal probability plot of difference in car mileage between Octane 87 and Octane 92 indicates the population could be normal and a boxplot indicated no outliers.

a. Express the null and alternative hypotheses in symbolic form for this claim. Assume μ¯d=μ1−μ2,μd¯=μ1-μ2, where μ1μ1 is the population mean mileage for Octane 87 and μ2μ2 is the mean mileage for Octane 92.

1) H0:μd¯

2) H1:μd¯

b. What is the significance level?

α=

c. What is the test statistic? Round to 3 decimal places.

d. What is the p -value? Round to 5 decimal places.

e. Make a decision.

• Reject the null
• Do not reject the null

f. What is the conclusion?

• There is sufficient evidence to support the claim that different octanes produce different miles per gallon.
• There is not sufficient evidence to support the claim that different octanes produce different miles per gallon.

Answer 1