Question

Suppose that 300 statistics students each took a random sample (with replacement) of 50 students at their college and recorded the ages of the students in their sample. Then each student used his or her data to calculate a 90 % the confidence interval for the mean age of all students at the college. How many of the 300 intervals would you expect to capture the true population mean age, and how many would you expect not to capture the true population mean? Explain by showing your calculation.

The number of intervals expected to capture the true population mean is

Answer 1

Interpretation of 90% confidence interval for population mean is : if we consider 100 independent samples from the same population , then 90 of the confidence intervals calculated using sample means will contain true population mean .

Thus out of 300 confidence intervals , 300*0.90 = 270 is expected to  capture the true population mean

Thus number of intervals expected to capture the true population mean is 270

And

number of intervals expected not to capture the true population mean is = 300-270 = 30