Five students took a math test before and after tutoring. Their scores were as follows.

Student	Before	After
A	65	78
B	68	76
C	56	63
D	75	73
E	80	87

a. At the 1% significance level, do the data provide sufficient evidence to conclude that the mean score before tutoring differs from the mean score after tutoring?

Hint: State Hypothesis, Compute test statistics, Find P-value, and Make decision.

b. Describe in the words of the problem what Type I and Type II errors are.