Question

Pro-choice/Pro-life and Region of the Country: The results of a 2013 Gallup poll about people's position on abortion (pro-life or pro-choice) by region of the country are summarized in the contingency table below.

Observed Frequencies: O_i's

	East	Midwest	South	West	Totals
Pro-Choice	208	111	169	191	679
Pro-Life	184	99	223	215	721
Totals	392	210	392	406	1400

The Test: Test whether or not there is a dependent relationship between abortion stance and region. Conduct this test at the 0.05 significance level.

(a) What is the null hypothesis for this test?

H₀: Opinion on abortion and region of the country are dependent variables.H₀: Opinion on abortion and region of the country are independent variables.     

(b) What is the value of the test statistic? Round to 3 decimal places unless your software automatically rounds to 2 decimal places.

χ²

=

(c) Use software to get the P-value of the test statistic. Round to 4 decimal places unless your software automatically rounds to 3 decimal places.
P-value =

(d) What is the conclusion regarding the null hypothesis?

reject H₀fail to reject H₀    

(e) Choose the appropriate concluding statement.

We have proven abortion stance and region are independent.The evidence suggests that there is a dependent relationship between abortion stance and region.    There is not enough evidence to conclude that there is a dependent relationship between abortion stance and region.

Additional Materials

Answer 1

Expected	East	midwest	south	west
Pro choice	392*679/1400=190.12	210*679/1400=101.85	392*679/1400=190.12	406*679/1400=196.91
Pro life	392*721/1400=201.88	210*721/1400=108.15	392*721/1400=201.88	406*721/1400=209.09

SD	East	midwest	south	west
Pro choice	(190.12-208)^2/190.12=1.682	(101.85-111)^2/101.85=0.822	(190.12-169)^2/190.12=2.346	(196.91-191)^2/196.91=0.177
Pro life	(201.88-184)^2/201.88=1.584	(108.15-99)^2/108.15=0.774	(201.88-223)^2/201.88=2.21	(209.09-215)^2/209.09=0.167

Test Statistic
The Chi-square test statistic is computed as follows
χ^2 = 1.682 + 0.822 + 2.346 + 0.177 + 1.584 + 0.774 + 2.21 + 0.167
χ^2 = 9.762

c)
The corresponding p-value of the test is p = P(χ^2 > 9.762) = 0.0207

d)
reject H0

e)
The evidence suggests that there is a dependent relationship between abortion stance and region.