Question

1. A researcher wants to determine if there is a significant difference between men and women in terms of guilty/non guilty pleas submitted by a sample of 50 defendants. Knowing that there are 25 women and 25 men in this sample and that 15 men entered guilty pleas [and 10 no guilty pleas] and 5 women entered guilty pleas [and 20 no guilty pleas]… [Hint: Calculated Chi-Sq. = 8.33]
2. 1. Formulate the null and research/alternative hypotheses.
   2. Create a contingency table with 2 rows and 2 columns based on the information provided.
   3. Calculate the chi-square
   4. Report the critical chi-square at the corresponding probability level [.05]and degrees of freedom
   5. Test the null hypothesis and reach a statistical conclusion
   6. Interpret your results [e.g., are men entering significantly more guilty pleas then women?]

Answer 1

null hypothesis: Ho: f there is no difference between men and women in terms of guilty/non guilty pleas

Alternate hypothesis:Ha: there is a significant difference between men and women in terms of guilty/non guilty pleas

2) contingency table:

Oi	male	female	Total
Guilty pleas	15	5	20
not Guilty pleas	10	20	30
total	25	25	50

3)

Applying chi square test:

Expected	Ei=row total*column total/grand total	male	female	Total
	Guilty pleas	10.00	10.00	20
	not Guilty pleas	15.00	15.00	30
	total	25	25	50
chi square    χ2	=(Oi-Ei)2/Ei	male	female	Total
	Guilty pleas	2.5000	2.5000	5.000
	not Guilty pleas	1.6667	1.6667	3.333
	total	4.167	4.167	8.333

test statistic X² =8.333

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 in critical region reject null hypothesis

we have suffiicent evidence to conclude that men are entering significantly more guilty pleas then women