Stat 101: Confidence intervals for the binomial

• Admistrivia
  • Homework due Friday by Noon.

Confidence intervals for binomials

• Gallup Poll: Forecast the presidential outcome
  • Not good enough to merely pick the winner.
  • The actual fraction is important also.
  • CI = p +/- 1.96 sqrt(p(1-p)/n)

• Literary Digest (Roosevelt vs Landon, 1936)
  • Largest opinion poll ever taken: 2.4 million
  • LD had been correct in every electin shince 1916
  • Predicted Roosevelt would get 42%
  • CI = 42% +/- .0006
  • Actual answer 62% for Roosevelt
  • sampling list came from: club membership lists, phone books (1/4 had phones)
  • Called "Selection bias"
  • Gallup predicted results using 50,000 people

• Typical current Gallup polls (see overhead)

• Problem: hard to find voters

Confidence intervals for small samples

• Problem: Manufacture good beer

• Solution: sample beer for various chemicals to see if it is done yet

• Difficulty: don't want to drink up all the beer!

• Solution: only take two observations

• See beer.jmp

• Suppose we want 99.8% accuracy, so we use +/- 3 SE's

• What happens? Try it in JMP.

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  Last modified: Mon Dec 6 13:21:36 EST 1999