For problem 16-24, suppose that it costs twice as much money to sample a child as the younger and older adults, where costs are the same per sampled person. The company believes that in the region of interest, 25% of the population is children, 55% are young adults, and 20% are older people. A proportional allocation of a total random sample of size 1,000 is undertaken, and people's responses on a scale of 0 to 100 are solicited. The results are as follows. For the children, x̄ = 90 and s = 5; for the young adults, x̄ = 82 and s = 11; and for the older people, x̄ = 88 and s = 6. Give a 95% confidence interval for the population average rating for the new chocolate.

Use the information in problem 16-24 (the weights and standard deviations) to determine an optimal allocation of the total sample.