A new method of postoperative treatment was evaluated for patients undergoing a certain surgical procedure. Under the old method, the mean length of hospital stay was 6.3 days. The sample mean for the new method was 6.1 days. A hypothesis test was performed in which the null hypothesis stated that the mean length of stay for the new method was greater than or equal to the mean length for the old method, and the alternative hypothesis stated that the mean stay for the new method was lower. The \(P\)-value was 0.002 . True or false:

a. Because the \(P\)-value is very small, we can conclude that the new method provides an important reduction in the mean length of hospital stay.

b. Because the \(P\)-value is very small, we can conclude that the mean length of hospital stay is less for patients treated by the new method than for patients treated by the old method.