Question: In a survey of a very large population, the incidences of two health problems are to be estimated from the same sample. It is expected that the first problem will affect about 3% of the population and the second about 40%. Ignore the finite population correction in answering the following questions.
a. How large should the sample be in order for the standard errors of both estimates to be less than .01? What are the actual standard errors for this sample size?
b. Suppose that instead of imposing the same limit on both standard errors, the investigator wants the standard error to be less than 10% of the true value in each case. What should the sample size be?