Suppose that 250 statistics students each tock a rancdom sample (with replacemen

Question

Suppose that 250 statistics students each tock a rancdom sample (with replacement) of 100 students at their college and recorded the ages of the students in their sample. Then each student used his or her data to caculate a 90% confidence interval for the mean age of all students at the college. How many of the 250 nten als would you expect to capture the true population mean age, and how many would you expect not to capture the true popuation mean? Explain by showing your calculation. The number of intervals expected to capture the true population mean is (Type aninteger or a decimal)

Explanation / Answer

Solution:

There are 250 statistics students each took a random sample of 100 students at their college and recorded the ages of the selected students. Then each student used his or her data for calculating 90% confidence interval for mean age of all students in their sample.
In this case, the proper interpretation of the given confidence level is in about 90% of all samples of 100 students, the resulting confidence interval will contain the mean age of all students.
Here, total number of confidence intervals = 250
The percentage of confidence level () = 90%

The expected numbers of intervals which capture the true population mean
= Total number of intervals x = 250 x 90% = 225

The expected numbers of intervals which do not capture the true population mean

=Total number of intervals x(100 - )% = 250 x 10%
= 25
Thus, the expected numbers of intervals which capture the true population mean is 225. Also, the expected numbers of intervals which do not capture the true population mean is 25.

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