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

c)H₀: there is no relationship between abortion stance and region of the country

d)H₁: there is a relationship between abortion stance and region of the country

e)

The value of expected frequency for each cell is given by,

And the table of expected frequency is,

	East	Midwest	South	West	Totals
Pro-Life	192.09	97.01	197.42	195.48	682
Pro-Choice	203.91	102.99	209.58	207.52	724
Totals	396	200	407	403	1406

f)

the test statistic is given by,

= 2.06+0.83+2.32+0.29+1.94+0.78+2.19+0.27 = 10.6961

g)p-value = 0.013488 {from chi-square table}

h)Since, P-value<0.10, we reject the null hypothesis that there is no relationship between abortion stance and region of the country.

i)the variables are dependent.

The probability that a person is pro-choice or pro-life depends on the region of the country where he/she lives or not.