A new method of teaching arithmetic to elementary school students was evaluated. The students who were taught by the new method were given a standardized test with a maximum score of 100 points. They scored an average of one point higher than students taught by the old method. A hypothesis test was performed in which the null hypothesis stated that there was no difference between the two groups, and the alternate hypothesis stated that the mean score for the new method was higher. The P-value was 0.001. True or false:

a. Because the P-value is very small, we can conclude that the mean score for students taught by the new method is higher than for students taught by the old method.

b. Because the P-value is very small, we can conclude that the new method represents an important improvement over the old method.