Question

On the most recent tax cut proposal, a random sample of Democrats and
Republicans in the Congress cast their votes as follows. Are the votes of Democrats and
Republicans independent of each other?
a. State the null and alternative hypotheses.
b. What is the test statistic?
c. Using a .05 significance level, what is the decision rule?
d. Show the test statistic and essential calculations.
e. Interpret you results

Favor    Oppose Abstain

85 78 37 Democrat

118    61 25 Republican

Answer 1

Since this is a test if the votes of Democrats and
Republicans independent of each other. So we will use a chi-square test for independence.

Observations	Favor	Oppose	Abstain	Total
Democrat	85	78	37	200
Republican	118	61	25	204
total	203	139	62	404

Expected value = Row total * Col total / Overall total

Eg: Expected Democrat and Favor = 200 * 203 / 404

Expected	Favor	Oppose	Abstain	Total
Democrat	100.495	68.812	30.693	200
Republican	102.505	70.188	31.307	204
total	203	139	62	404

a. State the null and alternative hypotheses.

:The votes of Democrats and Republicans are independent of each other

:The votes of Democrats and Republicans are not independent of each other

b. What is the test statistic?

Test Stat =

	Favor	Oppose	Abstain
Democrat	2.3891	1.2268	1.2960
Republican	2.3423	1.2028	1.2706

Test Stat = 9.7276

c. Using a .05 significance level, what is the decision rule?

Decision criteria: Reject the null hypothesis if |test Stat| > Critical value

d. Show the test statistic and essential calculations.

Critical value =

df = (no. of rows-1) * (no. of col -1)

= 2 * 1

= 2

At level of significance = 0.05

Critical value =

C.V. = 5.9915   ............using chi -square tables with df = 2 and p = 0.05

e. Interpret you results

Since Test Stat > C.V.

We reject the null hypothesis at 5% level of significance.

We conclude that the votes of Democrats and Republicans are not independent of each other.