STAT 3743 Daily Outline
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PANIC
If σ is unknown, use s instead
Remarks
- if n is large then approx 100(1 - α )% confidence
- if n small
– if pop'n normal then use Student's t critical value, get t-interval – if pop'n non-normal — if approx normal then still not too bad — if highly skewed or outliers, ask statistician
- can have one-sided intervals, too
Example: SRS(7) from pop'n, assume norm, find CI for μ
Confidence intervals for difference of two means
intuition for the confidence interval
First suppose variances known: two-sample z-interval
If variances are unknown:
- samples both large: use sample variances, approximate 100(1-α )% confidence
- one (or both) samples small, then in trouble unless
– pop'ns both normal — if variances equal: pooled t-interval — variances unequal: Welch interval
Example: independent SRS(4) and SRS(7), norm
Date: 2010-11-05 14:46:42 EDT
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