Question 1170547: If n=570 and ˆp (p-hat) = 0.57, construct a 99% confidence interval.
Give your answers to three decimals.
Answer by math_tutor2020(3816)   (Show Source):
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Given info:
n = 570 = sample size
phat = 0.57 = sample proportion
confidence level = 99%
At 99% confidence, the z critical value is roughly 2.576
Use a table or calculator to find this z critical value
E = margin of error
E = z*sqrt(phat*(1-phat)/n)
E = 2.576*sqrt(0.57*(1-0.57)/570)
E = 0.05341707292618
E = 0.053417
which is approximate
The confidence interval sets up an interval estimating the population parameter. In this case, we want to estimate the population proportion p
We are 99% confident that p is between the lower bound phat-E and upper bound phat+E
phat-E < p < phat+E
0.57-0.053417 < p < 0.57+0.053417
0.516583 < p < 0.623417
0.517 < p < 0.623
The 99% confidence interval is 0.517 < p < 0.623
We can rewrite that into the format (0.517, 0.623)
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