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Pro-choice/Pro-life and Region of the Country: The results of a 2013 Gallup poll about people's position...

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

  
  East     Midwest     South     West     Totals   
Pro−Choice     200   96     181     197     674   
Pro−Life     178   86     239     223     726   
Totals     378     182     420     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 test statistic? Round your answer to 3 decimal places.

χ2

=  

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

reject H0fail to reject H0     


(c) 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.

Solutions

Expert Solution

ho: there is a independent relationship between abortion stance and region

h1: there is a dependent relationship between abortion stance and region

a)

Observed Frequencies
Column variable
Row variable east mid west south west Total
pro choice 200 96 181 197 674
pro life 178 86 239 223 726
Total 378 182 420 420 1400
Expected Frequencies
Column variable
Row variable east mid west south west Total
pro choice 181.98 87.62 202.2 202.2 674
pro life 196.02 94.38 217.8 217.8 726
Total 378 182 420 420 1400
(fo-fe)^2/fe
1.784374 0.801465 2.22275 0.133729
1.656568 0.74406 2.063545 0.124151

chisq = sum(Oi-Ei)^2/Ei = 9.531

b)

df = (r-1)*(c-1)= (2-1)*(4-1) = 3

critical value, chisq(0.05, df) = 7.814

With chisq(3) > chisq(0.05, df), I reject the null hypothesis

c)

since ho is rejected, the conclusion is that there is a dependent relationship between abortion stance and region.

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

milcah answered 1 year ago
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