Key Terms
Confidence interval (CI) - an interval of the form
(point estimate - EBM, point estimate + EBM)
Use this when
Sigma is UNKNOWN and you are using s (sample standard deviation) as your estimate.
Distribution
Standard normal (Z).
CI
(p' - EBP, p' + EBP)
EXAMPLE
EBP = 0.03, CL = 90%, p' unknown z = 1.645 n = (1.645)^2 * (0.5)(0.5) / (0.03)^2 = 2.706 * 0.25 / 0.0009 = 751.67 -> rou
FORMULA
N = (z_(alpha/2))^2 * p'q' / EBP^2
RULE
Always round UP to the next whole integer. Rounding down gives a sample too small to meet the required precision.
Current practice
Use t-distribution any time s is used to estimate sigma, regardless of sample size.
Calculator
InvT(area to the left, df) For 95% CI: invT(0.975, df)
NOTATION
T ~ t_df where df = n - 1. Example: n = 20 -> df = 19 -> T ~ t_19
CI FORMAT
(x-bar - EBM, x-bar + EBM) -- same structure as z-interval.
Use when
The variable of interest is a count of successes out of n trials (yes/no, pass/fail, owns/doesn't own).
CONDITION TO USE THIS CI
Both n*p' >= 5 AND n*q' >= 5.
WHY IT EXISTS
The standard EBP formula uses p' and q' as estimates for p and q. This can introduce inaccuracy, especially for small sa
FIX
Pretend you have four extra observations -- two successes and two failures.