The instructor of an introductory organizational behavior course believes that there might be a relationship between the number of writing assignments (X) she gives in the course and the final grades (Y) earned by students in this class. She has taught this course with varying numbers of writing assignments for many semesters and has compiled relevant historical data in the file S04_61.xlsx.
a. Convert the given frequency table to a table of conditional probabilities of final grades (Y) earned by students in this class, given the number of writing assignments (X) in the course. Comment on the table of conditional probabilities. Generally speaking, what does this table tell you?
b. Given that this instructor requires only one writing assignment in the course, what is the expected final grade earned by the typical student?
c. How much variability exists around the conditional mean grade you found in part b? Also, what proportion of all relevant students earn final grades within two standard deviations of this conditional mean?
d. Given that this instructor gives more than one writing assignment in the course, what is the expected final grade earned by the typical student?
e. How much variability exists around the conditional mean grade you found in part d? What proportion two standard deviations of this conditional mean?
f. Find the covariance and correlation between X and Y. What does each of these measures tell you? In particular, is this instructor correct in believing that there is a systematic relationship between the number of writing assignments made and final grades earned in her classes?