Question

A random sample of 500 persons is questioned regarding their political affiliation and opinion on a tax reform bill. The observed contingency table is given below:

	Favored	Indifferent	Opposed	Row total
Democrat	138	83	64	285
Republican	64	67	84	215
Column total	202	150	148	500

1. Which variable can be reasonably thought of as the dependent variable, and which is the independent variable?
2. What is the probability that a person favored the tax reform bill, given that the person is a Democrat?
3. What is the probability that a person opposed the tax reform bill, given that the person is a Democrat?
4. What are the odds of favored versus opposed, given the person is a Democrat.
5. What are the odds of favored versus opposed, given the person is a Republican.
6. What is the odds ratio of favored versus opposed for a Democrat compared with a Republican? Express the odds ratio in words.
7. What is the probability that a person is a Democrat, given that person is indifferent to the bill?
8. Generate the expected values for this table based on a model of independence.

Answer 1

the probability distribution is given as

	Favored	Indifferent	Opposed	Row total
Democrat	0.276	0.166	0.128	0.57
Republican	0.128	0.134	0.168	0.43
Column total	0.404	0.3	0.296	1

(a) Dependent variable: opinion on a tax reform bill.  

Independent variable:political affiliation

(b) What is the probability that a person favored the tax reform bill, given that the person is a Democrat?

answer is 0.276/0.57=0.484

(c)What is the probability that a person opposed the tax reform bill, given that the person is a Democrat

answer is : 0.128/0.57=0.225

(d)What are the odds of favored versus opposed, given the person is a Democrat.

answer is:0.276/0.128=2.156

(e)What are the odds of favored versus opposed, given the person is a Republican.

answer is:0.128/0.168=0.762

(f)What is the odds ratio of favored versus opposed for a Democrat compared with a Republican? Express the odds ratio in words.

answer is : 2.156/0.762=2.829 which means democrat is 2.829 times more favor the tax reforms than republic

(g)What is the probability that a person is a Democrat, given that person is indifferent to the bill?

answer is 0.166/0.3=0.553

(h)Generate the expected values for this table based on a model of independence.

the expected value for this table is given as

	Favored	Indifferent	Opposed	Row total
Democrat	202*285/500=115.14	150*285/500=85.5	148*285/500=84.36	285
Republican	202*215/500=86.86	150*215/500=64.5	148*215/500=63.64	215
Column total	202	150	148	500