What about the sample size n for confi dence intervals for the difference of proportions p1 - p2? Let us make the following assumptions: equal sample sizes n = n1 = n2 and all four quantities n1p1, n1q1, n2p2, and n2q2 are greater than 5. Those readers familiar with algebra can use the procedure outlined in Problem 28 to show that if we have preliminary estimates 1 and 2 and a given maximal margin of error E for a specifi ed con fidence level c, then the sample size n should be at least
However, if we have no preliminary estimates for 1 and 2, then the theory similar to that used in this section tells us that the sample size n should be at least
(a) In Problem 17 (Myers-Briggs personality type indicators in common for married couples), suppose we want to be 99% confi dent that our estimate 1 - 2 for the difference p1 - p2 has a maximal margin of error E = 0.04. Use the preliminary estimates 1 = 289/375 for the proportion of couples sharing two personality traits and 2 = 23/571 for the proportion having no traits in common. How large should the sample size be (assuming equal sample size-i.e., n - n1 - n2)?
(b) Suppose that in Problem 17 we have no preliminary estimates for 1 and 2 and we want to be 95% con fident that our estimate 1 - 2 for the difference p1 - p2 has a maximal margin of error E = 0.05. How large should the sample size be (assuming equal sample size-i.e., n - n1 - n2)?
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