Question

Imagine that there are 100 different researchers each studying the sleeping habit of a college freshman. Each researcher takes a random sample size of 50 from the same population of freshman. Each researcher is trying to estimate the population mean hour of sleep freshman get at night, and each one construct a 95% confidence interval for the mean. Approximately how many of these 100 confidence will not capture the true mean

Answer 1

Approximately 5 intervals will not capture the true mean hour of sleep freshman get at night.

Explanation:

The (1 - α)% confidence interval for population mean implies that there is a (1 - α) probability that the true value of the mean is included in the interval.

Or, the (1 - α)% confidence interval for the mean implies that there is (1 - α)% confidence or certainty that the true mean value is contained in the interval.

And, if 100 such (1 - α)% confidence interval for the mean are computed then 95 of these 100 interval will consist of the true mean value.

In this case it is provided that 100 researchers estimate the population mean hour of sleep freshman get at night, and each one construct a 95% confidence interval for the mean.

Then approximately 95 of these 100 confidence intervals will capture the true mean hour of sleep freshman get at night. And approximately 5 intervals will not capture the true mean hour of sleep freshman get at night.