Question

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 School cost or Quality Convenience Other Totals Enrollment Status Full Time 421 393 76 890 Part Time 400 593 46 1039 Totals 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) Are the enrollment status and the reason for application independent? Explain using probabilities.

Answer 1

Following is the given table:

		School quality	School cost or convenience	Other	Totals
Enrollment status	Full time	421	393	76	890
	Part time	400	593	46	1039
	Totals	821	986	122	1929

(a)

To find the joint probability table for these data we need to divide each cell value by 1929. Following table shows the jotnt probability table rounded to 4 decimal places:

		School quality	School cost or convenience	Other	Totals
Enrollment status	Full time	0.2182	0.2037	0.0394	0.4614
	Part time	0.2074	0.3074	0.0238	0.5386
	Totals	0.4256	0.5111	0.0632	1

(b)

Column totals shows the marginal probabilities of school quality, school cost or convenience, and other. The marginal probabilities are:

	School quality	School cost or convenience	Other
Probability	0.4256	0.5111	0.0632

(c)

Out of 890 students goes full time, for 421 school quality is the first reason for choosing a school is

(d)

Out of 1039 students goes part time, for 400 school quality is the first reason for choosing a school is

(e)

Since so the enrollment status and the reason for application are not independent.