There are about 2,700 institutions of higher learning in the United States (inclduing junior colleges and community colleges). In 1976, as part of a continuing study of higher education, the Carnegie Commission took a simple random sample of 225 of these institutions. The average enrollment in the 225 sample schools was 3,700, with an SD of 6,000. A histogram for the enrollments was plotted and did not follow the normal curve. However, the average enrollment of all the 2,700 institutions was estimated to be 3,700, give or take 400 or so. Say whether each of the following statements is true or false, and explain why. a. It is estimated that 95% of the institutions in the United States enroll between 3,700-800 and 3,700+800=4,500 students.
b. An approximate 95%-confidence interval for the average enrollment of all 2,700 institutions runs from 2,900 to 4,500.
c. If someone takes a simple random sample of 225 institutions of higher learning, and goes 2 SEs either way from the average enrollment of the 225 sample schools, there is about a 95% chance that this interval will cover the average enrollment of all 2,700 schools.
d. The normal curve can't be used to figure confidence intervals here at all, because the data don't follow the normal curve.