Question

the gas mileage for a certain model of car is known to have a standard deviation of 5 mi/gal. a simple random sample of 64 cars of this model is chosen and found to have a mean gas mileage of 27.5 mi/gal. a 95% confidence interval for the mean gas mileage for this car model was calculated to be (26.775 mi/gal, 28.725 mi/gal). interpret the interval in words.
a if we took many samples like this one, 95% of them would find that 27.5 mi/gal is the mean gas mileage.
b the interval 26.775 to 28.725 miles per gallon will contain the true mean gas mileage for this model of car with a 0.95 probability.
c 95% of the cars have a true gas mileage between 26.775 and 28.725 miles per gallon.
d we are 95% confident that the true mean gas mileage for this model of car falls between 26.775 and 28.725 miles per gallon.
e there is a 95% chance that the true mean gas mileage for this model of car falls between 26.775 and 28.725 miles per gallon.

Explanation:

A confidence interval gives a range of values within which we are a certain percentage confident that the true population parameter lies. In the context of a 95% confidence interval for the mean gas - mileage, it means that if we were to take many samples and construct confidence intervals in the same way, about 95% of those intervals would contain the true population mean gas - mileage. It is not about the sample mean being a certain value in 95% of samples (option A is wrong), not about 95% of the cars having a gas - mileage in the interval (option C is wrong), and the language of "probability" for the true mean in a frequentist sense is not correct as the true mean is a fixed value (options B and E are wrong in their wording). Option D correctly interprets the 95% confidence interval as our level of confidence that the true mean gas - mileage lies within the given interval.

Answer:

D. We are 95% confident that the true mean gas mileage for this model of car falls between 26.775 and 28.725 miles per gallon.