Assume that a sample is used to estimate a population proportion p. Find the 90% confidence interval for a sample of size 248 with 120 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 = = x / n = 120 / 248 = 0.484
1 - = 1 - 0.484 = 0..516
Z/2 = 1.645
Margin of error = E = Z / 2 * (( * (1 - )) / n)
= 1.645 * (((0.484 * 0.516) / 248)
= 0.052
A 90% confidence interval for population proportion p is ,
- E < p < + E
0.484 - 0.052 < p < 0.484 + 0.052
0.432 < p < 0.536
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