Assume that a sample is used to estimate a population proportion
p. Find the 99% confidence interval for a sample of size
249 with 30 successes. Enter your answer as a tri-linear inequality
using decimals (not percents) accurate to three decimal
places.
Solution :
Given that,
Point estimate = sample proportion =
= x / n = 30 / 249 = 0.120
Z/2
= 2.576
Margin of error = E = Z
/ 2 *
((
* (1 -
)) / n)
= 2.576 * (((0.120
* 0.880) / 249)
= 0.053
A 99% confidence interval for population proportion p is ,
- E < p <
+ E
0.120 - 0.053 < p < 0.120 + 0.053
0.067 < p < 0.173
(0.067 , 0.173)
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