A Random Sample of 5726 Telephone Numbers from a Certain $p _ { 1 } = .20 \text { and } p _ { 2 } = .18$

question 13

Essay

A random sample of 5726 telephone numbers from a certain region taken in March 2002 yielded 1105 that were unlisted, and 1 year later a sample of 5384 yielded 980 unlisted numbers.
a. Test at level .10 to see whether there is a difference in true proportions of unlisted numbers between the two years.
b. If $p _ { 1 } = .20 \text { and } p _ { 2 } = .18$
what sample sizes (m = n) would be necessary to detect such a difference with probability .90?