Question

Suppose that 200 researchers are interested in studying the sleeping habits of college freshmen. Each researcher takes a random sample of size 80 from the same population of freshmen. Each researcher is trying to estimate the mean hours of sleep that freshmen get at night, and each one constructs a 90% confidence interval for the mean. Approximately how many of these 200 confidence intervals will NOT capture the true mean? (You do not need to do any complicated computations here!)

Answer 1

Solution,

The meaning of 90% confidence interval : 90% confidence interval means that there is 90% probability that the true population parameter will lie in the interval we constructed using 90% confidence level.

If we draw several samples of size n and we constructed the 90% confidence intervals using these samples , then 90% of these intervals will contain the true population parameter and 10 % of these intervals will not contain the true population parameter.

Here, 200 confidence intervals are constructed with 90%  confidence level.

90% of 200 = 180

10% of 200 = 20

So answer is 20

Approximately 20 of these confidence intervals will NOT capture the true mean