Question

Consider a 95% confidence interval for a population mean. Which of the following is not correct about the confidence interval?a.If we take random samples of same size from same population and compute confidence intervals, the center of each interval is equal to the population mean.b.If we take random samples of same size from same population and compute confidence intervals, about 95% of those intervals would capture the true mean of the population.c.If we take random samples of same size from same population and compute confidence intervals, the length of the interval remains the same for all intervals.d.If we take random samples of same size from same population and compute confidence intervals, about 5% of those intervals would miss the true mean of the population.

Answer 1

Given a 95% Confidence Interval, you need to remember that when you calculate a Confidence Interval for a mean of a population, this means that with a 95% of confidence the actual mean of that population is inside that interval.

Option a states that the center of the calculated interval is equal to the population mean. This is false because it is only possible to assure that the mean is inside that interval, but you do not know if it is in the center, to the right, or to the left.

Hence, the answer is: Option a.