Question

The following contingency table shows the number of people who took a statistics course classified by type of student and job outcome

                                                                                    Type of student

Job outcome                                                 Undergraduate (B₁)       Graduate (B₂)

Got a job after graduation(A₁)                                    150                             100

Did not get a job after graduation(A₂)                         50                             200

Are the two events in (d) independent? Show mathematically how you arrived at your conclusion.

Answer 1

Here we have to test that

Two events Type of student and Job outcome are independent.

Two events Type of student and Job outcome are not independent.

	B1	B2	Total
A1	150	100	250
A2	50	200	250
Total	200	300	500

Expected frequency = (Row total * Column total) / Grand Total

Observed freq(O)	Expected freq(E)	(O-E)
150	(250*200)/500 = 100	-50	2500	25
100	(250*300)/500 =150	50	2500	16.67
50	(250*200)/500 = 100	-50	2500	25
200	(250*300)/500 = 150	50	2500	16.67

Test statistic:

Degrees of freedom = (Number of rows - 1) * (Number of columns - 1)

                                 = (2 -1) * (2 - 1)

                                 = 1

alpha = 0.05        (If not given take it as 0.05)

Critical value for degrees of freedom = 1 and level of significance = alpha = 0.05 is

critical value = 3.84             (From statistical table of chi square values)

Here test statistic > critical value

so we reject H0.

Conclusion: Two events Type of student and Job outcome are not independent.