SOLUTION: Assume that a sample is used to estimate a population proportion p. Find the 90% confidence interval for a sample of size 95 with 31.6% successes. Enter your answer as a tri-linear

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Question 1204140: Assume that a sample is used to estimate a population proportion p. Find the 90% confidence interval for a sample of size 95 with 31.6% successes. Enter your answer as a tri-linear inequality using decimals (not percents) accurate to three decimal places.
< p <

Answer should be obtained without any preliminary rounding. However, the critical value may be rounded to 3 decimal places.
Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

phat = sample proportion = 0.316
phat's job is to estimate the population proportion p

n = sample size = 95

At 90% confidence, the z critical value is approximately z = 1.645
This is something to memorize.
Alternatively you can use a Z table or stats calculator (such as a TI83).

Then,
E = margin of error for a proportion
E = z*sqrt(phat*(1-phat)/n)
E = 1.645*sqrt(0.316*(1-0.316)/95)
E = 0.07846494809787
E = 0.078465 approximately

Afterward we compute the lower and upper bounds (L and U)
L = lower boundary
L = phat - E
L = 0.316 - 0.078465
L = 0.237535
L = 0.238

U = upper boundary
U = phat + E
U = 0.316 + 0.078465
U = 0.394465
U = 0.394

The 90% confidence interval in the format L < p < U would be approximately 0.238 < p < 0.394