Question

Lighter cars are more fuel-efficient than heavier cars. An environmentalist would like to estimate the true mean weight

of all cars. To do so, she selects a random sample of 30 cars and determines the 90% confidence interval for the true
mean weight to be 2.8 to 3.4 tons. Which of these statements is a correct interpretation of the confidence level?
O There is a probability of 0.90 that the confidence
interval (2.8, 3.4) captures the true mean weight of all cars.
O The environmentalist can be 90% confident that the true mean weight of all cars is between 2.8 and 3.4 tons,
O If many random samples of size 30 are selected from the population of all cars, approximately 90% of the sample
means will be between 2.8 and 3.4 tons.
O If many random samples of size 30 are selected from the population of all cars, about 90% of the intervals would
capture the true mean weight of all cars.

Answer 1

The environmentalist can be 90% confident that the true mean weight of all cars is between 2.8 and 3.4 tons.

Explanation:

x% confidence interval:

A confidence interval is built from a sample, has bounds a and b, and has a confidence level of x%. It means that we are x% confident that the population mean is between a and b.

In this question:

90% confidence interval between 2.8 and 3.4 tons. This means that the environmentalist can be 90% sure that the mean weight of all cars is in this interval, that is:

The environmentalist can be 90% confident that the true mean weight of all cars is between 2.8 and 3.4 tons.