Assume that a sample is used to estimate a population proportion p. Find the 98% confidence interval for a sample of size 176 with 114 successes. Enter your answer as an open-interval (i.e., parentheses) using decimals (not percents) accurate to three decimal places.
Given that,
Point estimate = sample proportion =
= x / n = 114 / 176 = 0.648
Z/2
= 2.326
Margin of error = E = Z
/ 2 *
((
* (1 -
)) / n)
= 2.326 * (((0.648
* 0.352) / 176)
= 0.084
A 98% confidence interval for population proportion p is ,
- E < p <
+ E
0.648 - 0.084 < p < 0.648 + 0.084
0.564 < p < 0.731
(0.564 , 0.731)
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