Math

The 112th Congress of the United States of America has 535 members, of which 87 are women. An alien lands near the US Capital and treats members of Congress as a random sample of the human race. He reports to his superiors the 95% confidence interval for the proportion of the human race that is female.

A) Calculate the confidence interval that the alien reports?

***Is it 13% to 19%????

B) What is wrong with the alien's approach to estimating the proportion of the human race that is female?

***It is not a randomized sample (although appears to be). Congress does not accurately reflect the overall population of women as Congress does not have many female members for one, and the sample does not include women from around the world.

Am I right? Thanks!

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asked by N
  1. The alien's report:

    The population of Earth is adequately large, we assume this is an SRS, and with p-hat being approximately .16, n*p-hat and n*(1 - p-hat) are both greater than 10. Therefore we can use the normal curve.

    We will use the confidence interval LaTeX: p-hat\:\pm z^{\cdot}\sqrt{\frac{p-hat\left(1-p-hat\right)}{n}} p − h a t ± z ⋅ p − h a t ( 1 − p − h a t ) n where p-hat = .1626, n = 535, and LaTeX: z^{\cdot} z ⋅ is 1.96.

    Our interval, then, is (.1314, .1939).

    We are 95% confident that the true proportion of Earth people who are women lies between 13% and 19%.

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    posted by N

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