As the U.S. population ages, the number of people needing medical care increases. Unless a cure is found in the next decade, one of the most expensive diseases requiring such care is Alzheimer’s, a form of dementia. To estimate the total number of Alzheimer’s cases in the future, a survey was undertaken. The survey determined the age bracket where 1 = 65–74, 2 = 75–84, 3 = 85 and over and whether the individual had Alzheimer’s (1 = no and 2 = yes). (Adapted from the Alzheimer’s Association, www.alz.org.)

 Here are the projections for the number of Americans (thousands) in each of the three age categories.

a. Determine the 95% confidence interval estimates of the proportion of Alzheimer’s patients in each of the three age categories.

b. For each year listed, determine 95% confidence interval estimates of the total number of Americans with Alzheimer’s disease.

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Age Category 2015 2020 2025 65-74 75-84 85+ 26,967 32,312 36,356 13,578 15,895 20,312 6,292 6,597 7,239