statistics 101

kinda funny...

from iowahawk:

Statisticians love balls and urns. A typical Stats 101 midterm, for example, usually includes a question along these lines:

"You take a simple random sample of 1000 balls from an urn containing 120,000,000 red and blue balls, and your sample shows 450 red balls and 550 blue balls. Construct a 95% confidence interval for the true proportion of blue balls in the urn."

After choking back a giggle about "blue balls," you whip out your calculator and text your frat brother who has a copy of last semester's midterm. He instantly recognizes the correct formula is

95% confidence interval for P = p +/- 1.96 * sqrt( p*(1-p) / n) * FPC



where P = the real, true, actual, honest-to-god proportion of blue balls in that great big f'ing urn
p = the sample proportion of blue balls, or 0.55
n = the sample size = 1000
FPC = the "finite population correction" = sqrt((N-n)/(N-1)) where N=120,000,000
and the 1.96 has something to do with the 95% probability area under a standard normal distribution

That second part, after the "+/-", is what you know as the "margin of error." Your frat brother texts you back and reminds you that since the population is very large, the FPC is very close to 1 and can be dropped. He also reminds you to uses the conservative estimate of p = 0.5 in the margin of error calculation, since you don't know the true value of p, only the sample estimate. So the whole formula simplifies to

p +/- 1.96 * sqrt( .25 / n)

=p +/- 0.98 / sqrt( n)


Assuming you still have juice in your calculator batteries and you're not hungover from the Sig Eps kegger last night, you should get

0.55 +/- 0.031


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