In an agricultural experiment, the effects of two fertilizers on the production of oranges were measured. Sixteen randomly selected plots of land were treated with fertilizer A. The average yield, in pounds, was 457 with a standard deviation of 38 . Twelve randomly selected plots were treated with fertilizer B. The average yield was 394 pounds with a standard deviation of 23. Find a \(99 \%\) confidence interval for the difference between the mean yields for the two fertilizers.