Question: For each of the following values for p^ and n, compute a 99% confidence interval for the

population proportion p using both the standard large-sample procedure and the WAC adjusted

procedure. Comment on whether the WAC adjustment was needed.

a. n = 20, ?p^?? = .35

b. n = 35, ?p^?? = .80

c. n = 50, ?p^?? = .34

d. n = 100, ?p^?? = .12

Answer:

a. it I Za/2 0.35 (0.65) n : 0.35 + 2.58 20 (0.0753,0.62517) WAC CI: y = y + 0.5za/2 = 10.3282 n = n+ Za/2 = 25.6564, it = = = 0.4026 n ni Za/2 it (1 - it) n = (0.1440,0.6309) The WAC procedure is preferred over the standard CI, except for exceptionally large sample sizes. b. Following the same procedure as above. WAC adjustment preferred. Lower Limit Upper Limit Large Sample Approx 0.6256 0.9744 WAC 0.5794 0.9247 c. Following the same procedure as above. WAC adjustment likely not needed. Lower Limit Upper Limit Large Sample Approx 0.1671 0.5138 WAC 0.1944 0.523 d. Following the same procedure as above. WAC adjustment likely not needed. Lower Limit Upper Limit Large Sample Approx 0.0362 0.2038 WAC 0.0561 0.2313