A polling firm randomly surveys 240 registered voters across the United States.
ID: 3311005 • Letter: A
Question
A polling firm randomly surveys 240 registered voters across the United States. Two of the survey questions ask respondents to state their gender (male or female) and their political affiliation (democrat, republican, independent, or other). The results of this survey are shown in the table below.
(a) Suppose we would like to perform a chi-square test to see if gender and affiliation are associated. Use = 0.1. What are the degrees of freedom for this test?
(b) Find the (standardized) residual for the female with Republican as their political affiliation. (Round your answers to three decimal places.)
(c) The residual shows that there were --- (more /fewer )---- females than expected.
(d) Given p-value is 0.001, what is the statistical decision?
Reject H0 and conclude that gender and political affiliation are independent.
Reject H0 and conclude that gender and political affiliation are associated.
Do not reject H0 and conclude that gender and political affiliation are associated.
Do not reject H0 and conclude that gender and political affiliation are independent.
Democrat Republican Independent Other Totals Female 72 46 22 3 143 Male 34 23 36 4 97 Totals 106 69 58 7 240Explanation / Answer
a)here for degree of freedom =(row-1)*(column-1) =(2-1)*(4-1)=3
b) for expected count of female with Republican as their political affiliation E =(row total*column total)/grand total
=69*143/240 =41.113
therefore standardized) residual =(O-E)/E1/2 =(46-41.113)/(41.113)1/2 =0.762
c_) residual shows that there were more females than expected.
d) as p value is ;ess then 0.1 level ; therefore
Reject H0 and conclude that gender and political affiliation are associated.