Question

Researchers studied the mean egg length​ (in millimeters) for a particular bird population. After a random sample of​ eggs, they obtained a​ 95% confidence interval of​ (45,60) in millimeters. In the context of the​ problem, which of the following interpretations is​ correct, if​ any?

A. We are 95% sure that an egg will be between 45 mm and 60 mm in length.
B. For this particular bird population, 95% of all birds have eggs between 45 mm and 60 mm.
C. We are 95% confident that the mean length of eggs for this particular bird population is between 45 mm and 60 mm.
D. We are 95% confident that the mean length of eggs in the sample is between 45 mm and 60 mm.
E. None of the above is a correct interpretation.

Answer 1

C. We are 95% confident that the mean length of eggs for this particular bird population is between 45 mm and 60 mm.

Explanation:

Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.

For 95% confidence interval, it means that we are 95% confident that the mean of the population is between the given upper and lower bounds of the confidence interval.

For the case above, the interpretation of the 95% confidence interval is that we are 95% confident that the mean length of eggs for this particular bird population is between 45 mm and 60 mm.