Question

which of the following would be a correct interpretation of a 99% confidence interval such as 4.1<μ<5.6?
choose the correct answer below.
○ a. we are 99% confident that the interval from 4.1 to 5.6 actually does contain the true value of μ.
○ b. it means that 99% of all data values are between 4.1 and 5.6.
○ c. it means that 99% of sample means fall between 4.1 and 5.6.
○ d. there is a 99% chance that μ will fall between 4.1 and 5.6.

Explanation:

A confidence interval gives a range of values within which we are confident the population parameter (here, \(\mu\)) lies. A 99% confidence interval means that if we were to take many samples and construct confidence intervals, about 99% of those intervals would contain the true population parameter.

• Option A: This is the correct interpretation. We are 99% confident that the interval \(4.1 <\mu<5.6\) contains the true value of \(\mu\).
• Option B: A confidence interval is about the population parameter (\(\mu\)), not about the data values.
• Option C: A confidence interval is not about sample means. It is about the population parameter.
• Option D: The population parameter \(\mu\) is a fixed value. It either is in the interval or not. We don't talk about a "chance" for a fixed parameter.

Answer:

A. We are 99% confident that the interval from 4.1 to 5.6 actually does contain the true value of \(\mu\)