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

Question

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

Quizplus · Accepted Answer

The correct interpretation of a confidence interval is that we are a certain percentage confident (in this case, 95%) that the true population mean falls within the interval. This does not mean that 95% of individual observations fall within this range, nor does it imply a probability statement about the population mean being in the interval after the data has been observed.

A Sample of 37 Light Bulbs Had a Mean Lifetime 579.2<μ<588.8579.2 < \mu < 588.8579.2<μ<588.8

A Sample of 37 Light Bulbs Had a Mean Lifetime $579.2 < \mu < 588.8$