:1a. Solution. Since this problem involves classifying and counting, we mark each ticket in the original box with a 0 or a 1. The tickets with a 4 on them are marked with a 1, the others with a 0. The number of 4's in the sample from the original box is like the sum of 100 draws from the new box. To find the SD of the new box, we need to know the fraction of 4's in the original box, but this is unknown. We estimate it as .2, the fraction of 4's in the sample. Similarly, the fraction of non-4's in the original box is estimated as .8. The SD of the new box is estimated by the bootstrap method as the square root of .2 x.8, or .4. The SE for the number of 4's in a sample of 100 is estimated as 10 x .4 = 4. This is 4% of 100, the size of the sample, so the SE for the percentage of 4's in the sample is estimated as 4. The estimate of the percentage of 4's in the box is the percentage of 4's in the sample, which is 20%. The lower endpoint of the 99.7% confidence interval is three SE's - as just computed - below this estimate, or 20% - (3 x 4%) = 20% - 12% = 8%.