Question

ou've surveyed all of the instructors in the CRMJ department at WSU asking what their current research interests are. They fall into these three categories: policing, corrections, courts. You want to know if the gender of the instructor affects their research interest. Of the women in the department, 10 are researching police, 8 are researching corrections, and 15 are researching courts. Of the men in the department, 16 are researching police, 10 are researching corrections, and 6 are researching courts. Set alpha to 0.05.

Identify the dependent and independent variables. Write out the null and alternative hypotheses. Calculate a test statistic, and interpret your results. Round all answers to 2 decimal points (0.00).

Answer 1

independent variables are gender of instructor

dependent variable research interest

Null : gender of instructor and research interest are independent

Alternate : gender of instructor and research interest are not independendent

This is chi-square test of independence problem

		c1	c2	c3	sum
	r1	10	8	15	33
	r2	16	10	6	32
	sum	26	18	21	65
	Eij	1	2	3
expected	1	13.2	9.138462	10.66154
	2	12.8	8.861538	10.33846
	Oi	10	8	15	16	10	6
	Ei	13.2	9.138462	10.66154	12.8	8.8615	10.338
								sum
	(Oi-Ei)^2/Ei	0.775758	0.141829	1.765435	0.8	0.1463	1.8206	5.450
							alpha	0.01
							critical value	9.210
							p-value	0.0655

TS = 5.450

df = (3-1)(2-1) = 2

critical value = 5.991   {=CHISQ.INV(1-0.05,2)}

since TS< critical value

we fail to reject the null hypothesis

we conclude that there is not evidence that both variable are not independent