Reading significance off a confidence interval

Question

A 95% confidence interval for the difference in mean return between two strategies (strategy B minus strategy A) is $[-0.5,\ 2.3]$ basis points.

At the 5% significance level, is the difference statistically significant? Explain using the interval.

Accepted Answer

Answer: no. The duality. A two-sided test at level \alpha and a 100(1-\alpha)\% confidence interval are two views of the same thing. A value c is rejected as the true parameter at level \alpha exactly when c falls outside the 100(1-\alpha)\% interval. Apply it. The null hypothesis of "no difference" is the value 0. Here 0 lies inside [-0.5, 2.3], so we fail to reject it. The data are consistent with zero difference at the 5% level; the result is not significant. Caution. Not significant does not mean the difference is zero. The interval also includes values as large as 2.3 bp, so a real and m…

Reading significance off a confidence interval

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