Confidence Intervals, Dynamics

How do confidence intervals change with confidence level, variance knowledge, and sample size?

Answer

We have the following:

  • Higher confidence level $\;\Rightarrow\;$ interval gets wider (more certainty requires more room). Holds generally.

  • Variance unknown $\;\Rightarrow\;$ use $t$-distribution instead of $z$ (interval gets wider; fatter tails). Holds in a "means" context.

  • Larger sample size $n \;\Rightarrow\;$ interval gets narrower (variance, hence std, decreases). Holds generally.

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