Question

Assume that a sample is used to estimate a population proportion p. Find the 98% confidence interval for a sample of size 108 with 25 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

Number of successes : x=25

Sample size : n = 108

Sample proportion of success := x/n = 25/108

Formula for  confidence interval estimate of a population proportion p

for 98% confidence level = (100-98)/100 =2/100 = 0.02

/2 =0.02/2 =0.01

Z_/2 = Z_0.01 = 2.326

98% confidence interval of a population proportion p =

98% C.I. = (0.137,0.326)