A sample of 37 AA batteries had a mean lifetime of 584 hours. A 95% confidence interval for the population mean was 579.2

Question

A sample of 37 AA batteries had a mean lifetime of 584 hours. A 95% confidence interval for the population mean was 579.2 < μ < 588.8. Which statements is the correct interpretation of the results?
A)We are 95% confident that the mean lifetime of all the bulbs in the population is between 579.2 hours and 588.8 hours.
B)The probability that the population mean is between 579.2 hours and 588.8 hours is 0.95.
C)95% of the light bulbs in the sample had lifetimes between 579.2 hours and 588.8 hours.
D)None of these statements correctly interpret the results.

Quizplus · Accepted Answer

A 95% confidence interval means that if we were to take multiple samples of the same size from the same population and calculate the mean lifetime of each sample, approximately 95% of those sample means would fall within the range of 579.2 to 588.8 hours. It does not mean that there is a 95% probability that the population mean falls within this range, nor does it describe the percentage of the sample that falls within this range. Therefore, option A is the correct interpretation.

A Sample of 37 AA Batteries Had a Mean Lifetime