Question

It is desired to estimate the proportion of individuals in a large population that carries at least one copy of an allele causing a certain genetic disorder. Call this population proportion ?. A simple random sample of 115 individuals is taken, and each is given a blood test. It is found that 3 individuals have at least one copy of the allele. Answer the questions below.

1. a) Is it possible to compute an estimate of ? from this data using the sample proportion as an estimator? Explain your answer. (You do not need to actually compute the estimate if you believe it is possible to do so.)

2. b) Is it possible to compute a valid CI for ? in this situation? Explain your answer. (You do not need to actually create the interval if you believe it is possible to do so.)

3. c) Regardless of your answers to (a) and (b), construct a 99% confidence interval for ?.

4. d) For a group of 1000 individuals from the same population, give a 99% confidence interval for the number of individuals who have at least one copy of the allele.

5. e) What is the appropriate sample size to construct a 99% confidence interval with a half-width of no more than 0.03 assuming you have no information about the population?

Answer 1