5. Some drivers with cars that can run on regular gas, buy premiu because they b

Question

5. Some drivers with cars that can run on regular gas, buy premiu because they believe that they will get better gas mileage. To test that belief, 10 drivers with cars that run on regular gasoline from a company fleet are recruited for an experiment. Each car is filled first with regular and the mileage for that tankful is recorded. Then the tank is filled with premium for the same 10 cars, and the mileage for that tankful is recorded. Here are the results (miles per gallon ): Car # Premium 19 22 24 24 25 25 26 26 28 32 Regular 16 20 21 22 23 22 27 25 27 28 Difference 323 2 23114 123 456 789 10 a. Compute a 95% lower bound for the average difference (premium-regular) in gas mileage. b. Use the confidence interval to answer the following question. Is there statistically significant evidence that the cars get better fuel economy with premium gasoline?

Explanation / Answer

Solution:

From the data
Difference 3, 2, 3, 2, 2, 3, -1, 1, 1, 4
now n = 10, mean x = 2, sd = 1.4142
95% confidence interval for the average difference (premium-regular) in gas mileage is:
= 0.05
Z/2 = 2.262
Standard error SE = sd/n = 1.4142/10 = 0.4472
Confidence interval CI = x ± Z/2 * SE
= 2 ± 2.262 * 0.4472
= (0.9884, 3.0115)

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