Stat 101: Confidence intervals

• Admistrivia
  • Do class evaluations

Confidence intervals--calculating them

• CI = estimate +/- 2 * SE

• SE is the standard deviation of the estimate

• Example: X-bar
  • SE = SD(X-bar) = sigma/sqrt(n)
  • So, CI = X-bar +/- 2 sigma/sqrt(n)

• Consider hits on my life calculator web page
  • Average age = 28.6, s = 19, n = 271
  • s/sqrt(n) = 1.15
  • CI = 28.6 +/- 2.3
  • CI = [26.3,29.9]
  • How do we interpret this?

• Interpretation: mu = average over year, CI constructed from one month
  • Naive interpretation: 95% chance that mu is in [26.3,29.9]
  • Classical interpretation: Interval is random and covers 95% of the time

• Technical details
  • If sigma is known use it: X-bar +/- 2 sigma/sqrt(n)
  • If sigma isn't known use st: X-bar +/- 2 s/sqrt(n)
  • Estimating proportions: pi-hat +/- 2 sqrt(pi(1-pi)/n)

Do we always use 2?

• For the MBA's, we always use 2

• For more sophisticated audiences--we use variants on 2
  • Example: 99.8% coverage needs 3
  • Example: 2/3 coverage needs 1
  • Example: exactly 95% needs 1.964
  • example: Psychological intervals are usually 50% which need +/- .67

• Other distributions require other numbers
• We will look at the t-distribution next time

Last modified: Wed Dec 1 10:08:28 EST 1999