52. A random sample of 5726 telephone numbers from a certain region taken in March 2002 yielded...

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52. 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 p1  .20 and p2  .18, what sample sizes (m 

n) would be necessary to detect such a difference with probability .90?

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