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.
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)
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