18. Because ethanol contains less energy than gasoline, a researcher wants to determine if the mileage of a car (y) is affected by the percent ethanol in the gasoline (x). The true population regression line relating the mean mileage y for a given ethanol content x (in percent) is μy|x = β0 + β1x. In a controlled environment, the mileage of a car is recorded when refueled 7 times using between 0% and 10% ethanol. The least squares regression line was found to be yˆ = βˆ0 + βˆ1x = 32.96 − 0.250x. We wish to test H0 : β1 = 0 versus Ha : β1 < 0="" at="" the="" α="0.05" significance="" level="" (i.e.="" we="" want="" to="" determine="" if="" the="" addition="" of="" ethanol="" significantly="" decreases="" mean="" gas="" mileage).="" what="" is="" the="" p−value="" for="" this="" test?="" what="" is="" your="" conclusion?="" note:="" s?e(βˆ1)="">
Which of the following is/are true?
(A) In reference to question (18), it would be appropriate to approximate the mean mileage when the car is using 85% ethanol
(B) In reference to question (18), a 95% confidence interval for β1 is (−0.375, −0.125)
(C) If two variables are correlated, then one must cause the other
(D) βˆ = Cov(x,y) (think carefully on this one) 1 s2x
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