Question

1. Your hapless statistics professor and the Center for Student Wellness have asked you to investigate the impact of winter weather on student mood. To study the topic, you collect information on the number of rainy days in each month and the number of symptoms of season affective disorder (SAD) students report experiencing at the end of the month.

              Student #      No. of rainy days               No. of symptoms of SAD

              1                                6                                  5

              2                                3                                  2

              3                                2                                  8

              4                                4                                  9

              5                                3                                  3

              6                                0                                  1

              7                                1                                  4

              8                                5                                 6

              9                                7                                  7

              10                              4                                  0                                                   

1. With a single statistic, summarize the strength and the direction of the association between the number of rainy days and the number of SAD symptoms experienced by students. Be sure to name and interpret the statistic you use.
2. Do your data provide enough evidence to conclude that the association between the weather and student mood in the population from which your sample was drawn? (Again, 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 will be using the sample correlation coefficient value to determine the strength and direction of the association. It is denoted by . We will use the CORREL function in MS Excel to calculate the value. Now, the value of = 0.38. This tells us that a below-average, positive association exists between the no. of rainy days and no. of symptoms of SAD. The association is loose and we can roughly say that as the no. of rainy days increase, the no. of symptoms of SAD also increases and vice versa.

(b) We are to test whether an association exists between the weather and the student mood in the population. Here, = population correlation coefficient.



We conclude that there is not enough evidence to suggest that an association exists between the weather and the student mood in the population. Here, = population correlation coefficient.