Confidence Intervals are often used and are a great way to not just give a point estimate but to tell where else the point might be. We will focus on confidence intervals based on normal data today.
z-confidence intervals for the mean
Suppose data with unknown mean but known variance. The confidence interval is then:
t-confidence intervals for the mean
Suppose where the mean and the variance are unknown. The confidence interval for the mean is:
. Where for T~t(n-1) and is the sample variance.
Chi-Square confidence intervals for the variance
Suppose and both, the mean and the variance are unknown. The confidence interval is:
where for .
Conservative normal confidence interval
Suppose are i.i.d. Bin(p) distributed. The conservative normal confidence interval is then: