A hybrid SUV A got a lot of attention when it first appeared. It is a relatively
ID: 3306569 • Letter: A
Question
A hybrid SUV A got a lot of attention when it first appeared. It is a relatively high-priced hybrid SUV that makes use of the latest technologies for fuel efficiency. One of the more popular hybrid SUVs on the market is the modestly priced hybrid SUV B. A consumer group was interested in comparing the gas mileage of these two models. In order to do so, each vehicle was driven on the same 10 routes that combined both highway and city streets. The results showed that the mean mileage for SUV A was 27mpg and SUV B was 33 mpg. The Standard deviations were 3.8 mpg and 2.8 mpg respectively.
1) An analyst for the consumer group computed the two-sample t 95% confidence interval for the difference between the two means as ( 5.175, 6.825). What conclusion would he reach based on his analysis?
A.
He is not given enough information to make any conclusions.
B.
He can conclude a statistically significant difference in fuel economy.
C.
He can conclude that, statistically, there is no significant difference in fuel economy.
D.
He cannot discern a statistically significant difference in fuel economy.
2) Why is this procedure inappropriate? What assumption is violated?
A. It was assumed the data are dependent, but they are not because the two vehicles were driven at two separate time periods.
B. It was assumed the data are independent, but they are not because the two vehicles were driven over the same 10 routes.
C. It was assumed the data are independent, but they are not because the two vehicles were driven by the same driver.
D. It was assumed the data are dependent, but they are not because the two vehicles were made by different manufacturers.
3) In what way do you think this may have impacted the results?
A. The analyst came to the wrong conclusion because of his assumption errors.
b. The analyst performed the wrong test because of his assumption errors.
c. It may have made it more difficult to distinguish a difference.
d. It would have made it easier to distinguish a difference.
Explanation / Answer
Solution:-
1) B) He can conclude a statistically significant difference in fuel economy.
Since 95% confidence interval does not contain 0 hence there is statistically significant difference in fuel economy.
2) C. It was assumed the data are independent, but they are not because the two vehicles were driven by the same driver.
3) b. The analyst performed the wrong test because of his assumption errors.
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