Question

1. At a Midwestern University the 450 students in the Business School were classified according to their major within the business school and their gender. The results are:   

	Female	Male	Total
Accounting	68	56	124
Administration	91	40	131
Economics	5	6	11
Finance	61	59	120
Other	39	25	64
Total	264	186	450

1. Complete a table for marginal distribution.
2. Complete a table for Conditional distribution

Answer 1

Solution:

Given: At a Midwestern University the 450 students in the Business School were classified according to their major within the business school and their gender.

	Female	Male	Total
Accounting	68	56	124
Administration	91	40	131
Economics	5	6	11
Finance	61	59	120
Other	39	25	64
Total	264	186	N = 450

Part a) Complete a table for marginal distribution.

We divide each frequency by N = 450 in above table.

Major    Gender	Female	Male	Marginal distribution of Major
Accounting	0.151111	0.124444	0.275556
Administration	0.202222	0.088889	0.291111
Economics	0.011111	0.013333	0.024444
Finance	0.135556	0.131111	0.266667
Other	0.086667	0.055556	0.142222
Marginal distribution of Gender	0.586667	0.413333	1

Part b) Complete a table for Conditional distribution

Conditional distribution Major Given Gender:

Formula for conditional probability is:

Then

Similarly we find all conditional probabilities:

	P(Major |Female)		P(Major |Male)
P(Accounting | Female)=	0.257576	P(Accounting | Male)=	0.301075
P(Administration | Female)=	0.344697	P(Administration | Male)=	0.215054
P(Economics | Female)=	0.018939	P(Economics | Male)=	0.032258
P(Finance | Female)=	0.231061	P(Finance | Male)=	0.317204
P(Other | Female)=	0.147727	P(Other | Male)=	0.134409

Conditional distribution Gender given Major:.

Similarly we find all probabilities:

	P(Female | Major)		P(Male |Major)
P(Female|Accounting)=	0.548387	P(Male|Accounting)=	0.451613
P(Female|Administration)=	0.694656	P(Male|Administration)=	0.305344
P(Female|Economics)=	0.454545	P(Male|Economics)=	0.545455
P(Female|Finance)=	0.508333	P(Male|Finance)=	0.491667
P(Female|Other)=	0.609375	P(Male|Other)=	0.390625