The statistics professor wants to examine the relationship between the studying hours of students along with his or her test grade. Suppose a sample of 5 students is selected.

StudentsStudying hours (x)Test grade (y)

1 1470

2 1595

3 6 40

4 850

5 11 88

a. Calculate and interpret the correlation coefficient.

b. Perform a hypothesis test to determine if the population correlation coefficient () is significantly different from zero [ = 0.05]. (Note: one tail question) .Hint: first, set the hypothesis, Second: Find test Statistic for the Correlation Coefficient, Third: find the critical t-score, Forth: set the conclusion

c. Estimate the regression equation (calculate0and 1) and write the regression equation.

d. What is the predicted number of test grade for a student with 6 studying hours? In other word if x = 6 in the regression equation, what is the value of .

e. Calculate the upper and lower confidence level. Assume the = 3.951 , contract /2 =2.776 for x=6.