A mean daily return of 3 basis points has a different meaning when its standard error is 1 basis point rather than 10. A point estimate needs an uncertainty calculation. This lesson derives normal-family pivots, constructs confidence intervals, and tests whether a mean return differs from zero. It separates statistical evidence from economic value and explains the assumptions behind the error bars.
Learning objectives. By the end of this note you should be able to:
- state the sampling laws of and under i.i.d. normal data, and form a interval for ;
- construct a large-sample (Wald) interval for a mean or a Bernoulli ;
- formulate vs , define Type I/II errors and -values, and avoid treating significance as a trading signal;
- test whether a mean return differs from zero and interpret the result cautiously.
In this lesson
- Sampling distributions in the normal family
- Confidence intervals
- Hypothesis testing framework
- The significance trap
- Duality of intervals and tests
Before you start
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