Question 1085 • English Language Arts 10 - Second Semester
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?
Answer
A
There is a probability of 0.90 that the confidence interval (2.8, 3.4) captures the true mean weight of all cars.
B
The environmentalist can be 90% confident that the true mean weight of all cars is between 2.8 and 3.4 tons.
C
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.
D
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.
Explanation
A 90% confidence level describes how often the interval-making method succeeds over repeated random samples. If many samples of 30 cars are taken and a confidence interval is calculated from each, about 90% of those intervals will contain the true mean weight of all cars. Choice B describes confidence in this particular interval, but D states the meaning of the confidence level most precisely.
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