In a survey of MBA students, the following data were obtained on "students" first reason for application to the school in which they matriculated."
|
|
Reason for application
|
|
|
|
|
School quality
|
school cost
|
Other
|
Total
|
|
Enrollment
|
Full time
|
421
|
393
|
76
|
890
|
|
status
|
part time
|
400
|
593
|
46
|
1039
|
|
Total
|
821
|
986
|
122
|
1929
|
a) Develop a joint probability table for these data.
b) Use the marginal probabilities of school quality, school cost or convenience, and other to comment on the most important reason for choosing a school.
c) If a student goes full time, what is the probability that school quality is the first reason for choosing a school?
d) If a student goes part time, what is the probability that school quality is the first reason for choosing a school?
e) Let A denote the event that a student is full time and B denote the event that the student lists school quality as the first reason for applying. Are events A and B independent? Justify your answer.