A polling firm randomly surveys 230 registered voters across the United States.
ID: 3309879 • Letter: A
Question
A polling firm randomly surveys 230 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 Other as their political affiliation. (Round your answers to three decimal places.)
(c) The residual shows that there were (___) fewer more females than expected. Fill in blank.
(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 68 44 20 6 138 Male 33 20 33 6 92 Totals 101 64 53 12 230Explanation / Answer
Ans:
a)degree of freedom=(4-1)*(2-1)=3
b)
d)p-value=CHIDIST(15.747,3)=0.001
As,p-value<0.1,we reject null hypothesis.
Reject H0 and conclude that gender and political affiliation are associated.
Observed(O) Democrat Republican Independent Other Totals Female 68 44 20 6 138 Male 33 20 33 6 92 Totals 101 64 53 12 230 Expected(E) Democrat Republican Independent Other Totals Female 60.6 38.4 31.8 7.2 138 Male 40.4 25.6 21.2 4.8 92 Totals 101 64 53 12 230 (O-E)^2/E Democrat Republican Independent Other Female 0.904 0.817 4.379 0.200 Male 1.355 1.225 6.568 0.300 Total chi square score=15.747