Question

8. The success of a federally funded, locally administered manpower program was measured by the propor- tion of clients who moved from subsidized employment into unsubsidized (private sector) employment and remained there for a certain length of time. A random sample of n = 376 clients of the program produced the following results this question is worth 4 marks). Failure 19 Education 8 years or less 9 to 11 years 12 years 13 years or more Success 13 76 107 32 45 19 i. Estimate the marginal probabilities of success and failure. ii. Test the hypothesis that the program outcomes are independent of educational level using a X2 test of independence.

Answer 1

(i)

Given the above table, the marginal probability of success =

13+ 76 + 107 + 32 = = 0.6064 376

The marginal probability of failure=

19+45 +65 + 19 2 = 0.3936 376

(ii)

To test the significance of independence is as follows:

education	Success	Failure
8 years or less	13 (19.40)[2.11]	19(12.60)[3.26]
0 to 11 years	76(73.37)[0.09]	45(47.63)[0.14]
12 years	107(104.30)[0.07]	65(67.70)[0.11]
13 years or more	32(30.93)[0.04]	19(20.07)[0.06]

chi-square statistic turns out to be 5.8817. The p-value is 0.117511. Therefore, we fail to reject the null hypothesis, thus, education turns out to have no significant impact on outcomes.