Pro-choice/Pro-life and Region of the Country: The results of a 2013 Gallup poll

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: Oi's

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.

2 =  

(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.

East Midwest South West Totals Pro-Choice   208   111     175     184     678   Pro-Life   184   99     231     208     722   Totals   392     210     406     392     1400  

Explanation / Answer

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

b)aplying chi square test of independence on above:

2 = 9.98

c) p value =0.0188 ( please try 0.0187 if this does not work due to rounding)

d)

as p value is higher then 0.01 level

fail to reject H0  

e)

There is not enough evidence to conclude that there is a dependent relationship between abortion stance and region.

Observed O east midwest south west Total pro-choice 208 111 175 184 678 pro-life 184 99 231 208 722 Total 392 210 406 392 1400 Expected E=rowtotal*column total/grand total east midwest south west Total pro-choice 189.840 101.700 196.620 189.840 678 pro-life 202.160 108.300 209.380 202.160 722 Total 392 210 406 392 1400 chi square =(O-E)^2/E east midwest south west Total pro-choice 1.7372 0.8504 2.3773 0.1797 5.145 pro-life 1.6313 0.7986 2.2324 0.1687 4.831 Total 3.368 1.649 4.610 0.348 9.9756

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