Question

A social worker has been asked to testify before her state legislature about the impact of long-term foster care on child outcomes in government spending. She has the following figures

a. Conduct the contingency test my setting up the hypothesis and decision rule. What can you conclude from this test? What should be the social worker testimony?

	In Prison	Not in Prison
Remain in the foster system	300	200
Adopted	200	600

Answer 1

Answer:

The null and alternate hypothesis are:

H0: Being in prison or not is independent of remaining in the foster system.
Ha: Being in prison or not is not independent of remaining in the foster system.

Now, Expected frequency = [(Row total) x (Column total)] / Table total

Expected frequency:

	In prison	Not in prison	TOTAL
Remain		307.69	500
Adopted	307.69	492.31	800
TOTAL	500	800	1300

Test statistic value =

Let the level of significance be 5%.

The critical value is given by:

Since the test statistic value is greater than the critical value, so we have sufficient evidence to reject null hypothesis H0.

Thus, we can conclude that being in prison or not is not independent of remaining in the foster system.

So, the social worker's testimony should be that the children who are adopted are less likely to be in prison.

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