A public agency is interested in learning more about the persons living in nursing homes in a particular city. A total of 100 nursing homes are caring for 4800 people in the city and a cluster sample of six homes has been taken. Each person in the six homes has been interviewed. A portion of the sample results follows.

a. Develop an estimate of the mean age of nursing home residents in this city.
b. Develop an approximate 95% confidence interval for the proportion of disabled persons in the city's nursing homes.
c. Estimate the total number of disabled persons residing in nursing homes in this city.

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Average Age of Residents Home Residents 61 74 78 69 73 84 Disabled Residents 12 30 10 14 96 23 71 29