In the bootstrap examples, exactly 30 observations have been repeatedly resampled from the original sample. The choice of 30 was given because the original sample had 30 observations. If we had resampled 3 observations instead, the resampled \(\hat{p}^*\) value could have ranged from 0 to 1 (producing a much larger \(SE(\hat{p}^*)\) than desired). If we had resampled 300 observations instead, the resampled \(\hat{p}^*\) value would have been close to the same number each time (producing a much smaller \(SE(\hat{p}^*)\) than desired).

Generally, if \(n\) represents the size of the original sample, how many observations should we resample with replacement when bootstrapping?

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