8.91 Unequal sample sizes

You are planning a survey in which a 95% confidence interval for the difference between two proportions will present the results. You will use the conservative guessed value 0.5 for and in your planning. You would like the margin of error of the confidence interval to be less than or equal to 0.10. It is very difficult to sample from the first population, so that it will be impossible for you to obtain more than 25 observations from this population. Taking , can you find a value of that will guarantee the desired margin of error? If so, report the value; if not, explain why not.