:

(121/400) x 100% = .3025 x100% = 30%

approximately. We need the SE for the number of white flower seeds in a sample of 400. Suppose we have a box of 10,000 tickets, one for each seed in the box described in the problem. Now mark each ticket with a 1 if the corresponding seed for a white flower, 0 if it is for a red flower. The number of white flower seeds oi a sample of 400 from the original box is like the sum of 400 draws from this new box. To find the SE of the sum of these draws we need to know the proportion of 1's in the new box, that is, the proportion of white flower seeds in the original box. We don't know this, so we estimate it by the fraction of white flower seeds in the sample, which is about .30. The SD of the 0-1 box is the square root of .3 x .7 = .21, or .46. The SE of the sum of the draws (assuming the draws are without replacement) is 20 x .46 = 9.2. The draws are with replacement, so we multiply by the correction factor, which is equal to the square root of 9600/9999 = .96, or .98, and get an SE of 9.0. This is the SE of the number of white flower seeds in a sample of 400 from the box. The SE of the percentage of white flower seeds is (9.0/400)x100% = 2.25% (without the correction factor we get an SE of 2.3%). : from 28% to 32%. (Without the correction factor the interval runs from 30 - 2.5 % to 30 + 2.5%, or 27.7% to 32.5%.)