91Ó°ÊÓ

A random sample of 100 students from a large college showed an average IQ score of 112 with a standard deviation of 10 . (a) Establish a 95 confidence interval estimate of the mean IQ score of all students attending this college. (b) Establish a \(.99\) confidence interval estimate of the mean IQ score of all students in this college.

Nine students living on the third floor in Burton Hall at Oberlin College did their laundry an average of 19 times during the academic year. Their standard deviation was \(2.7\) washes. Establish a 95 confidence interval estimate of the average number of times a year an Oberlin student launders his clothes.

Derive a method for determining a \(100(1-\alpha) \%\) confidence interval for the unknown variance, \(\sigma^{2}\), of a normal distribution when the mean is also unknown.

In a public opinion poll, 320 out of 400 persons interviewed supported the administration's policy on disarmament. (a) Establish a \(95 \%\) confidence interval estimate of the proportion of persons supporting the government's stand on disarmament. (b) What can be concluded with \(.99\) confidence about the maximum error in our estimate if the proportion of those supporting the administration policy is estimated as \(80 \%\) ? (c) With what degree of confidence can we assert that the proportion of persons supporting the administration policy is somewhere between \(77 \%\) and \(83 \% ?\)