Question

study of career plans of young women and men sent questionnaries to all 722 membwrs of the senior class in the college and business adminstration at the university of illnois. one questin asked which major within the business program the students had chosen. here are the data from the students who responded:

Female Male

Accounting 68 56

Administration 91 40

Economics 5 6

Finance 61 59

a) find the two marginal distributions

b) find the conditional distributions of major for men and women

c) what percent of students did not respond to the questonaire

Answer 1

Let F be Female , M be Male , A be Accounting , Ad be Administration , E be Economics , Fi be Finance.

a) P( F) = 225 / 722 = 0.3116

P( M ) = 161 / 722 = 0.2230

P( A ) = 124 / 722 = 0.1717

P( Ad ) = 131 / 722 = 0.1814

P( E ) = 11 / 722 = 0.0152

P( Fi ) = 120 / 722 = 0.1662

b) Conditional distributions :

P( A | F ) = 68 /225 = 0.3022

P( Ad | F ) = 91 / 225 = 0.4044

P( E | F ) = 5/225 =0.0222

P( Fi | F) = 61 / 225 = 0.2711

P( A | M ) = 56 / 161= 0.3478

P( Ad | M ) = 40/161 = 0.2484

P( E | M ) = 6/161 =0.0373

P( Fi | M) = 59/161 = 0.3665

P( F | A ) = 68/124 = 0.5484

P( F | Ad ) = 91 / 131 = 0.6947

P( F | E ) = 5/11 = 0.4545

P( F | Fi ) = 61 / 120 = 0.5083

P( M | A ) = 56/124 = 0.4516

P( M | Ad ) = 40/ 131 = 0.3053

P( M | E ) = 6/11 = 0.5455

P( M | Fi ) = 59 / 120 = 0.4917

c) Percent of students did not respond to the questionnaries = ( 722 - 386 ) / 722

= 336/722

= 0.4654

46.54% of students did not respond to the questonaire.