A statement that “the 95% confidence interval for the population mean is (275, 325)" means that 95% of the population values are between 275 and 325. Is this true/false? & Why?

Question

I think the statement is false but I am not sure so I can't come up with a reason/rationale. Thank you

Answer 1

False. The confidence interval is for the probability that the interval captures the population mean. This was usually obtained by taking a number of samples and using their means and standard deviation in order to generate the confidence interval around the mean of sample means that captures 95% of the data. If the population mean is not equal to the mean of sample means, this would NOT capture 95% of the population.