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?
choose the correct answer below.
a. for this particular bird population, 95% of all birds have eggs between 45 mm and 60 mm.
b. we are 95% confident that the mean length of eggs for this particular bird population is between 45 mm and 60 mm.
c. we are 95% confident that the mean length of eggs in the sample is between 45 mm and 60 mm.
d. we are 95% sure that an egg will be between 45 mm and 60 mm in length.
e. none of the above is a correct interpretation.

Explanation:

A confidence interval is an estimate for the population parameter (in this case, the population mean egg length). It does not refer to individual eggs (so options A and D are wrong as they talk about individual eggs or 95% of birds' eggs). Also, the confidence interval is for the population mean, not the sample mean (so option C is wrong as it refers to the sample mean). Option B is correct as it states that we are 95% confident about the population mean (the mean length of eggs for the particular bird population) being within the interval (45,60).

Answer:

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