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Statistics
Confidence Intervals
October 9, 2008
Outline
1. A 95% confidence interval for µ is
σ
x̄ ± 1.96 √
n
2. Conditions for inference: normal distribution of population variable, SRS, known σ.
(a) What if the population variable is not normal?
(b) What if the sample is not an SRS?
(c) What if σ is not known?
3. If σ is not known, use s, the sample standard deviation, to estimate it.
x̄ − µ
√
σ/ n
has a standard normal distribution but
x̄ − µ
√
s/ n
has a t-distribution with n − 1 degrees of freedom.
4. The confidence interval now becomes
s
x̄ ± t∗ √
n
where t∗ is the appropriate critical value for the t distribution, use Table C.