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. Here, the population parameter is the true mean gas mileage of the car model. A 95% confidence interval 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.

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.