Build the interval from an estimate and its error

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An estimated edge is 2.4 basis points with a standard error of 1.0 basis point, and the sampling distribution is approximately normal. Build the 95% confidence interval, decide whether the edge is significant at 5%, and estimate the two-sided p-value.

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Build the interval. An approximate 95% confidence interval is the estimate plus or minus 1.96 standard errors: 2.4 \pm 1.96 	imes 1.0 = [0.44,\ 4.36]. Read significance. The interval [0.44,\ 4.36] excludes the null value 0, so the edge is significant at the 5% level. Estimate the p-value. The z-statistic is the estimate divided by its standard error: z = \frac{2.4}{1.0} = 2.4, \qquad p = 2\,[1 - \Phi(2.4)] = 2 	imes 0.0082 = 0.0164 \approx 0.016. This is consistent with the interval: since p \approx 0.016 is below 0.05, the 95% interval had to exclude 0, and since it is above 0.01, the 99% …

Build the interval from an estimate and its error

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