:3a. There are about 2,700 institutions of higher learning in the United States (including 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 size 225 from these institutions. The average enrollment of the institutions in the sample was 3,700, with an SD of 6,000.
A histogram for the enrollments was plotted and did not follow the normal curve.
(i) If someone takes a simple random sample of 225 institutions of higher learning, and goes two SE's 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 2700 schools.
(ii) The normal curve can't be used to figure confidence intervals here at all, because the data does not follow the normal curve.
Which of the following holds?
a. both (i) and (ii) are true
b. (i) is true, but (ii) may not be
c. (ii) is true, but (i) may not be
d. both (i) and (ii) are false