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?