Question

Assume that a sample is used to estimate a population proportion p. Find the 98% confidence interval for a sample of size 194 with 21% successes. Enter your answer as an open-interval (i.e., parentheses) using decimals (not percents) accurate to three decimal places.

Answer 1

Solution :

Given that,

Point estimate = sample proportion = = 0.21

Z_/2 = 2.326

Margin of error = E = Z _{/ 2} * (( * (1 - )) / n)

= 2.326 * (((0.21 * 0.79) / 194)

= 0.068

A 98% confidence interval for population proportion p is ,

- E < p < + E

0.21 - 0.068 < p < 0.21 + 0.068

0.142 < p < 0.278

(0.142 , 0.278)