Consider the poor alien who got an awful estimate of the proportion of females i

Question

Consider the poor alien who got an awful estimate of the proportion of females in the world by using the U.S. Senate as its sample. Suppose that the alien, having learned to distinguish male and female names, decides to use a page from a telephone book as its sample. Select one page from the white pages of a telephone book. (I put the numbers of females/males below).

Disregard all listings of businesses, listings which provide only initials, and listings with first names that are not gender-specific (like Pat or Fran). For the listings that you can reasonably identify as male or female, count how many are male and how many are female. Record these values.

What is the sample proportion of females in your sample? Female=157 Male=201

Use your sample data to form a 95% confidence interval for the actual proportion of all humans who are female.

Does this confidence interval provide a reasonable estimate of the actual proportion of all humans who are female? If not, explain why the confidence interval procedure fails in this situation.

Suggest a practical method for the alien to choose a sample which is likely to produce a reasonable estimate of the proportion of women among the human population.

Explanation / Answer

p = 157 / ( 157+201) = 0.44

alpha / 2= 0.025 Z= 1.96

confidence interval

0.44 +/- 1.96 * srqt (0.44*0.56 / 358 )

0.44 +/- 0.0514

0.3886 < p < 0.4914

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