Confidence Intervals for a Proportion

Question

Assume that a sample is used to estimate a population proportion p. Find the 98% confidence interval for a sample of size 357 with 286 successes. Enter your answer as an open-interval (i.e., parentheses) using decimals (not percents) accurate to three decimal places.

98% C.I. = 

Answer should be obtained without any preliminary rounding. However, the critical value may be rounded to 3 decimal places.

Answer 1

CI interval for a proportion = sample proportion (phat) +/- z-critical * sqrt(phat*(1-phat)/sample size))

Phat = 286/357 = 0.8

z-critical is z-score associated with (1 + 0.98/2) = 0.99 probability = 2.33

CI = 0.8 +/- 2.33 * sqrt(0.8*0.2/357)

= 0.8 +/- 0.049

= (0.751,0.849)