# Confidence intervals how to find?

1. Mar 2, 2005

### semidevil

so if I want to find the 90% confidence interval..how do I do it?

all I know is that given 220 salads, 179 were contaminated.

i'm asked to find the 90% confidence interval, the true proportion of the contimatned salads.

so the formula is 100(1- a)% confidnece =[(y - z(a/2) * sigma/root(n)), ((y + z(a/2) * sigma/root(n)].

so my a is .9 right? since I am looking for 90%? so do I just do Z(.9/2) and look at the table?

what about n and sigma? n is 220, and what is sigma? what about the y's

Last edited: Mar 2, 2005
2. Mar 2, 2005

### juvenal

Are you familiar with the binomial distribution? I think that's what you want to use to get your sigma (= standard deviation).

3. Mar 2, 2005

### xanthym

Consider the sample of 220 salads to be 220 independent events having the Binomial Distribution. The proportion "p" of contaminated salads will then be Binomially Distributed:
{Observed Proportion} = p = (179/220) = (0.8136)
{Estimated Proportion Std Dev} = sqrt{p(1 - p)/N} = sqrt{(0.8136)(1 - 0.8136)/220) = (0.02626)

Because sample size is large, the Binomial Distr of "p" is approximated by the Normal Distr of "p" having the same Mean and Std Dev. For a 2-Tailed 90% (Normal Distr) Confidence Interval on the Population Proportion μ:
Prob{(-1.645) < Z < (+1.645)} = 0.90
Prob{(-1.645) < {(0.8136) - μ}/(0.02626) < (+1.645)} = 0.90
Prob{(0.8568) > μ > (0.7704)} = 0.90

90% Confidence Interval for Population Proportion μ is (0.7704, 0.8568)

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Last edited: Mar 2, 2005
4. Dec 12, 2009

### LMLuis06

how did you go from Prob{(-1.645) < {(0.8136) - μ}/(0.02626) < (+1.645)} = 0.90 to Prob{(0.8568) > μ > (0.7704)} = 0.90 ?

5. Dec 12, 2009

### LMLuis06

How can i work on this one? I have been stuck for 2 hours: BRCA 1 is a gene that has been linked to breast cancer. Researchers used DNA analysis to search for BRCA 1 mutations in 169 women with family histories of breast cancer. Of the 169 women tested, 27 has BRCA 1 mutations. Let p denote the probability that a woman with a family history of breast cancer will have a BRCA 1 mutation. Find a 95% confidence interval for p.