Question

A researchers want to know if gender and having health care as a primary voting issue is related. They survey 275 Americans of voting age and the results are summarized in the table below. Is there sufficient evidence to determine if gender and health care as a primary voting issue are related?

....................................................Male | Female | Total

Health Care Primary Issue............{69} | {72} | {141}

Health Care Not Primary Issue.....{81} | {53} | {134}

Total..............................................{150} | {125} | {275}

(a) State the null and alternative hypotheses.

(b) Calculate the values for the labeled cells of the following table of expected values. Round your answers to one decimal place.

..................................................(Male) {Female}

Health Care Primary Issue .......(——-) {Cell 1}

Health Care Not Primary Issue (Cell 2) {——–}

Work for Cell 1

Work for Cell 2

(c) Calculate the degrees of freedom.

(d) Calculate the test static χ 2 (chi-squared).

(e) Using α = 0.050 as the level of significance and given that the critical value for the test is χ 2 0.050 = 3.841 should the researchers accept or reject the null hypothesis? Why or why not

Answer 1

a)

Null hypothesis: Ho: gender and health care as a primary voting issue are independent

Alternate hypothesis Ha: gender and health care as a primary voting issue are related

b)

Expected	Ei=row total*column total/grand total	male	female
	Primary issue	76.9	64.1
	not primary issue	73.1	60.9

c)

degree of freedom(df) =(rows-1)*(columns-1)=(2-1)*(2-1)=

1

d)

Applying chi square test of independence:

chi square    χ2	=(Oi-Ei)2/Ei	male	female	Total
	Primary issue	0.813	0.976	1.7894
	not primary issue	0.856	1.0270	1.8828
	total	1.6692	2.0030	3.672
test statistic X2 =		3.672

e)

since test statistic does not falls in rejection region we fail to reject null hypothesis