Assume that a sample is used to estimate a population proportion
p. Find the 99% confidence interval for a sample of size
305 with 168 successes. Enter your answer as an
open-interval (i.e., parentheses) using
decimals (not percents) accurate to three decimal places.
C.I. =
Solution :
Given that,
Point estimate = sample proportion = = x / n = 168 / 305 = 0.551
1 - = 1 - 0.551 = 0.449
Z/2 = 2.576
Margin of error = E = Z / 2 * (( * (1 - )) / n)
= 1.645 * (((0.551 * 0.449) / 305)
= 0.073
A 99% confidence interval for population proportion p is ,
- E < p < + E
0.551 - 0.073 < p < 0.551 + 0.073
0.478 < p < 0.624
C.I. = 0.478 , 0.624
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