Question

Assume that a sample is used to estimate a population proportion p. Find the 80% confidence interval for a sample of size 380 with 125 successes. Enter your answer as an inequality using decimals (not percents) accurate to three decimal places.

Answer 1

The sample proportion is computed as follows, based on the sample size N = 380 and the number of favorable cases X = 125: X P= N 125 = 380 = 0.329 The critical value for a = 0.2 is ze = 21-a/2 = 1.282. The corresponding confidence interval is computed as shown below: CI (Proportion) = (o-zvo(1, p) + ze v (19.))

0.329(1 -0.329) 0.329 - 1.282 x V - 4.0.329 + 1.282 380 V 0.329(1 -0.329) 380 = (0.298, 0.36)

80% confidence interval is 0.298 < p < 0.360