Question

Sam computed a 95% confidence interval for μ from a specific random sample. His confidence interval was 10.1 < μ < 12.2. He claims that the probability that μ is in this interval is 0.95. What is wrong with his claim?

Answer 1

Either is in the interval or it is not. Therefore, the probability that is in this interval is 0 or 1.

Answer 2

The sample mean will vary from sample to sample. A 95% confidence interval for the population mean is an interval that on average will contain the population mean in 95 out of every 100 such intervals. The other 5 intervals will not contain the population mean. Therefore it is not correct to assign a probability value to a confidence interval calculated from a specific random sample.