A large population of interest is known to be comprised of 50% females, 50% males. A study is being planned to estimate the average annual income in this population. The study team suspects that:

1. the average annual female and male incomes differ by $ ;
2. the variance of female incomes is $\times10^6$ (dollars-squared);
3. the variance of male incomes is $\times10^6$ (dollars-squared).

(a) Based on these suppositions, how much of a reduction in confidence interval width would you anticipate if you carry out a stratified sample using proportional allocation rather than a simple random sample (with the same total sample size in either case)? Express your answer as a percent reduction, to one decimal place. (For instance, if the ratio of the two interval widths happened to be 0.6, you would enter an answer of 40.0, since this corresponds to a 40.0 percent reduction.)

(b) Based on these suppositions, how much of a reduction in confidence interval width would you anticipate if you carry out a stratified sample using optimal allocation rather than a stratified sample using proportional allocation (with the same total sample size in either case)? Again express your answer as a percent reduction, to one decimal place.