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	200	96	169	211	676
Pro-Life	178	86	223	237	724
Totals	378	182	392	448	1400

The Test: Test whether or not there is a dependent relationship between abortion stance and region. Conduct this test at the 0.01 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 H₀

fail 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.

Answer 1

using minitab>stat>tables>chi square test for association

we have

Chi-Square Test for Association: data, Worksheet columns

Rows: data Columns: Worksheet columns

East Midwest South West All

Pro-Choice 200 96 169 211 676
182.5 87.9 189.3 216.3
1.6741 0.7503 2.1729 0.1308

Pro-Life 178 86 223 237 724
195.5 94.1 202.7 231.7
1.5631 0.7005 2.0288 0.1222

All 378 182 392 448 1400

Cell Contents: Count
Expected count
Contribution to Chi-square

Pearson Chi-Square = 9.143, DF = 3, P-Value = 0.027
Ans a )

the null hypothesis is

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

(b) the value of the test statistic χ² =9.14

(c)the P-value of the test statistic =0.027

(d) since p value is less than 0.05 so

reject H₀

(e)

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