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	104	169	197	678
Pro-Life	184	92	223	223	722
Totals	392	196	392	420	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.

Answer 1

Null Hypothesis : The abortion stance and region are dependent. (i.e) there is a statistically significant difference between the abortion stance and the region.

Test statistic will be the omnibus chi-square statistic.

=9.879 ; p-value = 0.0196

Since the p-value is less than 0.05. we reject the null hypothesis. We conclude that there is no statistically significant difference between the abortion stance and the region. The abortion stance and region are independent.