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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. Use the information in problem 16–24 (the weights and standard deviations) to determine an optimal allocation of the total sample.
Cadbury, Inc., is interested in estimating people’s responses to a new chocolate. The company believes that people in different age groups differ in their preferences for chocolate. The company believes that in the region of interest, 25% of the population are 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, = 90 and = 5; for the young adults, = 82 and = 11; and for the older people, = 88 and = 6. Give a 95% confidence interval for the population average rating for the new chocolate.