Question

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

	East	Midwest	South	West	Totals
Pro-Life	212	106	176	188	682
Pro-Choice	184	94	231	215	724
Totals	396	200	407	403	1406

Express any probabilities (p-value) rounded to 3-significant digits.

Test whether or not there is a dependent relationship between abortion stance and region of the country. Conduct the test at the 0.01 significance level.

a) What is the n?

b) What is the df?

c) What is the null hypothesis? (Be specific - don't use generic wording.)

d) What is the alternate hypothesis? (Again, be specific - don't use generic wording.)

e) Calculate the expected frequencies, keeping the data organized in table format.

f) Calculate the chi-squared test statistic. Show your work.

g) Calculate the p-value.

h) Make a decision about whether to reject or fail to reject the null hypothesis by comparing the p-value to the criterion level. Again, make sure you avoid using generic wording. What specific null hypothesis are we rejecting or failing to reject?

i) Make a concluding statement about whether the variables are dependent or not. Be specific: Is the probability that a person is pro-choice or pro-life dependent on the region of the country where he/she lives or not?

Answer 1

a) n= 1406

b) D.f= (k-1)(m-1)= (2-1)(4-1)= 3

c) Null Hypothesis H0: Relationship between abortion stance and region of the country is independent.

d) Alternative Hypothesis Ha: Relationship between abortion stance and region of the country is dependent.

e) Pro-life (East)= 396*682/1406= 192.085

Pro-Life (Mid West)=200*682/1406=97.013

Pro-life (South)= 407*682/1406 =197.421

Pro-life (West)= 403*682/1406= 195.481

Pro-Choice (East)= 396*724/1406= 203.915

Pro-Choice (Mid West)=200*724/1406= 102.987

Pro-Choice (South)= 407*724/1406 = 209.579

Pro-Choice (West)= 403*724/1406= 207.519

Abortion/Region	Observed	Expected
Pro-life (East)	212	192.085
Pro-life (Midwest)	106	97.013
Pro-life (South)	176	197.421
Pro-life (West)	188	195.481
Pro-Choice (East)	184	203.915
Pro-Choice (Midwest)	94	102.987
Pro-Choice (South)	231	209.579
Pro-Choice (West)	215	207.519
Total	1406	1406

f) chi square= summation(Oi-Ei)^2/Ei

= 10.696

g) The P-Value is 0.013 The result is significant at p < 0.05

h) Since P value is significant. Reject null hypothesis H0 that relationship between abortion stance and region of the country is independent at 0.05 level of significance.

i) Conclusion: Relationship between abortion stance and region of the country are dependent.