Question

d. (2 point) There are 255 students this term completing this same assignment. Assuming they calculated the CI correctly, how many students should we expect to have an interval that does not contain the true mean?

So after I took a random simple sample of 45 / 900 data points, I found the 90% CI. What is the solution to finding out how many students would have found an interval that doesn't include the population mean in it?

Answer 1

Total number of students = 255

Confidence level = 90%

Interpretation of Confidence Interval:

If repeated samples are taken and the 90% Confidence Interval is computed for each sample,, 90% of the intervals will contain the population mean.

Thus,

Number of students we expect to have an interval that contains the true mean = 255 X 90/100 = 229.5

So,

Number of students we expect to have an interval that does not contain the true mean = 255 - 229.5 = 25.5 = 26 (Round to integer)

So,

Answer is:

26