The table provides data on gender and college for the students is one section of

Question

The table provides data on gender and college for the students is one section of the course Introduction to Computer Science. In the table, we have used the abbreviations BUS for Business, ENG for Engineering and Applied Sciences, and LIB b. Determine the conditional distribution of gender within each college and the marginal distribution of gender. c. Determine the conditional distribution of college within each gender and the marginal distribution of college. d. Does an association exist between the variables "gender" and "college" for this population? Yes No

Explanation / Answer

I am going to first count the number of various data given here.

M+BUS = 3

M+ENG = 5

M+LIB = 3

F+BUS =3

F+ENG = 2

F+LIB = 4

Total sample size = 20. To find the probability of any group just divide the number with 20.

For example for a female taking business the probability is 3/20 = 0.15

b.

c.

e.

We have,

and

Thus we get the chi-square value as 1.24. With 2 degrees of freedom the corresponding P-value is 0.54 which is quite high. Thus there must not be any association between these variables.

BUS ENG LIB Total M 0.15 0.25 0.15 0.55 F 0.15 0.10 0.20 0.45 Total 0.30 0.35 0.35 1.00

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