In: Statistics and Probability
Assume that a sample is used to estimate a population proportion
p. Find the 95% confidence interval for a sample of size
252 with 79% successes. Enter your answer as a tri-linear
inequality using decimals (not percents) accurate to three decimal
places.
< p <
Solution :
Given that,
Point estimate = sample proportion =
= 0.79
1 -
= 1 - 0.79 = 0.21
Z/2
= 1.96
Margin of error = E = Z
/ 2 *
((
* (1 -
)) / n)
= 1.96 * (((0.79
* 0.21) / 252)
Margin of error = E = 0.050
A 95% confidence interval for population proportion p is ,
- E < p <
+ E
0.79 - 0.050 < p < 0.79 + 0.050
0.740 < p < 0.840