A sample of 36 light bulbs had a mean lifetime of 508 hours. A 95% confidence interval for the population mean was $500.8

Question

A sample of 36 light bulbs had a mean lifetime of 508 hours. A 95% confidence interval for the population mean was $500.8 < \mu < 515.2$ Which one of the following statements is the correct interpretation of the results?
A) 95% of the light bulbs in the sample had lifetimes between 500.8 hours and 515.2 hours
B) None of these are true.
C) We are 95% confident that the mean lifetime of all the bulbs in the population is between 500.8 hours and 515.2 hours.
D) The probability that the population mean is between 500.8 hours and 515.2 hours is 0.95.

Quizplus · Accepted Answer

The confidence interval is a range of values that is likely to contain the true population mean with a certain degree of confidence. The correct interpretation of a 95% confidence interval is that we can be 95% confident that the true population mean falls within the interval. Therefore, choice C is the correct interpretation. Choice A is incorrect because the confidence interval is not a statement about individual bulbs in the sample. Choice D is also incorrect because the probability refers to the long-term frequency of the event, whereas the confidence interval pertains to a single unknown value (the population mean).

A Sample of 36 Light Bulbs Had a Mean Lifetime 500.8<μ<515.2500.8 < \mu < 515.2500.8<μ<515.2

A Sample of 36 Light Bulbs Had a Mean Lifetime $500.8 < \mu < 515.2$