Question

Suppose that we wish to estimate the population mean grade-point average (GPA) across all UVA undergraduate students. From a simple random sample of 50 undergraduate students, a 95% confidence interval for the population mean GPA is (2.9, 3.6). Which of the following is a correct interpretation of the confidence interval?

A: There is a 95% probability that the population mean GPA is between 2.9 and 3.6.
B: If repeated samples of size n = 50 were selected, then the population mean GPA would fall between 2.9 and 3.6 approximately 95% of the time.
C: If repeated samples of size n = 50 were selected, then 95% of confidence intervals computed from these sample means would include the population mean GPA.
Both B and C are correct interpretations.
A, B, and C are all correct interpretations.

Answer 1

The correct interpretation is C: If repeated samples of size n = 50 were selected, then 95% of confidence intervals computed from these sample means would include the population mean GPA.

Explanation: A confidence interval is a range of values that is likely to contain the true population parameter with a certain level of confidence. In this case, the 95% confidence interval (2.9, 3.6) means that if we were to take repeated samples of size 50 and compute confidence intervals for each sample, we would expect 95% of these intervals to include the true population mean GPA.

Option A is incorrect because a confidence interval is not a statement about the probability of a parameter falling within the interval.

Option B is incorrect because it assumes that the population mean GPA will fall between 2.9 and 3.6 approximately 95% of the time, which is not necessarily true.

Option D is incorrect because B is not a correct interpretation - option B assumes that the population mean GPA will fall between 2.9 and 3.6 approximately 95% of the time, which is not necessarily true.