Question

1. (-/10 Points] DETAILS 0/2 Submissions Used MY NOTES PRACTICE ANOTHER 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. Democrat Republican Independent Other Totals Female 66 43 20 5 134 Male 36 21 33 6 96 Totals 102 64 53 11 230 (a) Suppose we would like to perform a chi-square test to see if gender and affiliation are associated. Use a = 0.1. What are the degrees of freedom for this test? (b) Find the (standardized) residual for the female with Independent as their political affiliation. (Round your answers to three decimal places.) (c) The residual shows that there were fewer females than expected in the Independent category. (d) Given p-value is 0.003, what is the statistical decision? Reject Ho and conclude that gender and political affiliation are independent. Reject Ho and conclude that gender and political affiliation are associated. Do not reject Ho and conclude that gender and political affiliation are associated. Do not reject Ho and conclude that gender and political affiliation are independent. Submit Answer Viewing Saved Work Revert to Last Response

Answer 1

(a) degrees of freedom = ( number of rows -1) *( number of columns-1)

= ( 2-1) *(4-1)

= 3

(b) Expected female in the independent category is

Ei =134*53/230 = 30.8783 (Expected frequency= row total *column total / grand total)

Residual is given by

$ri=\frac{Oi-Ei}{\sqrt{Ei}}$

For female in independent category , Oi = 20 , Ei = 30.8783

Thus ,

$ri=\frac{20-30.8783}{\sqrt{30.8783}}= -1.958$

(c) The residual shows , there are fewer females than expected in the independent category

(d) P value = 0.003

As P value < 0.1 , reject H0

Answer is

Reject H0 and conclude that gender and political affiliations are associated .