This exercise relates to the illustrative example on screening for twins discussed in Section 6.5. White female-female pairs were constructed as described in the illustrative example on the basis of same date of birth and SS#'s matching on the first seven digits. The number of pairs so constructed is as follows:

Quartile Based on SS#

Sequence Difference First quartile Middle two quartiles Fourth quartile Number of Pairs Constructed from Medicare Files 10,024 20,031 10,024 Suppose that you guess that the overall prevalence of twins among these pairs is 20%, and that the prevalence of twins in the first quartile is twice that in the second quartile, while it is three times that in the third quartile. If you are planning to take a stratified random sample of 300 pairs from this file for the purposes of estimating the prevalence of twins in this file, what would be the optimal allocation in each of the three quartiles?

Suppose that instead of a stratified random sample of 300 pairs, it is decided to take a simple random sample of 300 pairs and the following data are obtained:

a. What is the estimated prevalence of twins and its standard error?

b. Find the poststratified estimate of the prevalence of twins and its standard error.