Of the 1,395 colleges in the United States, 364 have 2-year programs and 1,031 are 4-year schools. In a random sample of forty 2-year schools, it was found that the text Statistics Can Be Fun, by A. N. Optimist was used in ten of the schools. In an independent random sample of sixty 4-year schools, this text was used by eight of the sample members.

(a) Find an estimate of the proportion of all colleges using Optimist's text, using an unbi- ased estimation procedure.

(b) Find a 95% confidence interval for the proportion of all colleges using this text.