A statistics instructor at a large western university would like to examine the relationship (if any) between the number of optional homework problems students do during the semester and their final course grade. She randomly selects 5 students for study and asks them to keep track of the number of these problems completed during the course of the semester. At the end of the class each student's total is recorded along with their final grade.  For the following data, draw a scatter plot, calculate the regression equation, and conduct a six-step hypothesis test to determine whether problems completed positively predicts students' final grades.