Question

3. A researcher wants to know if there is a relationship between having death-penalty statutes and having three-strikes laws in place. Based on the information regarding these laws in US states…[Hint: calculated chi-square should be 4.160]

	Death Penalty
Three-strikes law	Yes	No
Yes	19	2
No	19	10

1. Formulate the null and research/alternative hypotheses.
2. Calculate the chi-square
3. Report the critical chi-square at the corresponding probability level [.05]and degrees of freedom
4. Test the null hypothesis and reach a statistical conclusion;
5. Interpret your results

Answer 1

null hypothesis: Ho: having death-penalty statutes and having three-strikes laws in place are independent

Alternate hypothesis:Ha: there is a relationship between having death-penalty statutes and having three-strikes laws in place.

applying chi square test:

Expected	Ei=row total*column total/grand total	Yes	No	Total
	Yes	15.96	5.04	21
	No	22.04	6.96	29
	total	38	12	50
chi square    χ2	=(Oi-Ei)2/Ei	Yes	No	Total
	Yes	0.5790	1.8337	2.413
	No	0.4193	1.3278	1.747
	total	0.998	3.161	4.160

chi-square test statistic X² =4.160

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

1

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

3.841

as test statistic is higher than critical value we reject null hypothesis

we have sufficient evidence to conclude that there is a relationship between having death-penalty statutes and having three-strikes laws in place.