Question

One year, there were about 3,000 institutions of higher learning in the U.S. including community colleges and junior college. As part of a continuing study of higher education, the Carnegie Commission took a simple random sample of 400 of those institutions. The average enrollment in the 400 sample schools was 3,700, and the standard deviation was 6,500. Find a 68% confidence interval for the average enrollment of all 3.000 institutions. (You may assume that the box is NOT lopsided)

Answer 1

Formula for Confidence Interval for Population mean when population Standard deviation is not known

Given
Sample Mean : : Sample average enrollment	3700
Sample Standard Deviation : s	6500
Sample Size : n : Number of institutions in the random sample	400
Degrees of freedom : n-1	399
Confidence Level :	68
= (100-68)1/00	0.32
/2	0.16
	0.9957

68% confidence interval for the average enrollment of all 3.000 institutions

68% confidence interval for the average enrollment of all 3.000 institutions = (3376.3975,4023.6025)