1. Work-related disease may low the quality of life of workers and increase heal

Question

1. Work-related disease may low the quality of life of workers and increase health related cost. We are interested in estimating the proportion of workers p suffered by occupational diseases in a business of 1000 workers. (a) It is expected that about 5% of workers may have a certain form of work-related disease. Based on the simple random, obtain n to have the standard deviation of the sample proportion less than 2%. (b) Also, what will be the required n to obtain the standard deviation of the sample total is only 10% of the true total?

Explanation / Answer

a) sqrt(p * (1 - p)/n) = 0.02

or, sqrt(0.05 * 0.95/n) = 0.02

or, sqrt(n) = sqrt(0.05 * 0.95)/0.02

or, sqrt(n) = 10.9

or, n = 119

b) sqrt(p * (1 - p)/n) = 0.1

or, sqrt(0.05 * 0.95/n) = 0.1

or, sqrt(n) = sqrt(0.05 * 0.95)/0.1

or, sqrt(n) = 2.18

or, n = 5

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