Question

A local town is considering a budget proposal that would allocate tax dollars toward the renovation of a new police station. A survey is conducted to measure public opinion concerning the proposal. A total of 150 individuals respond to the survey: 50 who report being republican and 100 who report being democrat. The frequency distribution is as follows:

Opinion

Favor          Oppose

Republican	35	15
Democrat	55	45

- Based on these results, is there a significant difference in the distribution of opinions for republicans versus democrats? Test at the .05 level of significance.

- Compute the phi-coefficient to measure the strength of the relationship.

Answer 1

null hypothesis: Ho: there is no difference in distribution of opinions for republicans versus democrats

alternate hypothesis:Ha: there is a significant difference in the distribution of opinions for republicans versus democrats

degree of freedom(df) =(rows-1)*(columns-1)=

1

for 1 df and 0.05 level of significance critical region       χ2=

3.841

applying chi square test:

Expected	Ei=row total*column total/grand total	Favour	Oppose	Total
	Republican	30.00	20.00	50
	Democrats	60.00	40.00	100
	total	90	60	150
chi square    χ2	=(Oi-Ei)2/Ei	Favour	Oppose	Total
	Republican	0.8333	1.2500	2.083
	Democrats	0.4167	0.6250	1.042
	total	1.250	1.875	3.125

as test statistic 3.125 is not higher than critical value; we fail to reject null hypothesis

we do not have sufficient evidence to conclude that there is a difference in the distribution of opinions for republicans versus democrats

b)

phi coefficient =sqrt(X²/n)=sqrt(3.125/150)=0.14