Question

1. In preparing for an examination, some students in a class studied more than others. Each student's grade on a 10-point exam and the number of hours studied are as follows:

                        Student                   Hours Studied      Exam Grade                     

                        Barbara                      4                          5

                        Bob                             1                          2

                        Diane                          3                          1

                        Owen                         5                          5

                        Charles                      8                          9

                        Ed                               2                          7

                        Sanford                      7                          6

                        Summer                     6                                  8

1. Calculate the Pearson's correlation coefficient for the association between study time and the grade earned.
2. Provide an interpretation for the correlation coefficient.
3. Do the sample data provide sufficient evidence with which to conclude that a real association exists in the population from which this sample was drawn? (To answer this question, you will need to perform a hypothesis test.) Explain your answer and show all necessary work. You should write out the research and null hypotheses in Greek notation.

Answer 1

(a) We input the data set in Excel and use the CORREL function to compute the correlation coefficient value. The value = 0.6832.

(b) This correlation coefficient value tells us that there is a moderate, positive association between the variables Hours Studied and Grade. This further tells us that as the number of hours studied increases, the grades also increase and vice versa.

(c) We are to test whether there exists a real association between Hours Studied and Grade. Here, = population correlation coefficient.