Question

****OPTIONS FOR C: FEWER OR MORE

A polling firm randomly surveys 210 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 61 39 19 3 122 Male 33 18 32 5 88 Totals 94 57 51 8 210 (a) Suppose we would like to perform a chi-square test to see if gender and affiliation are associated. Use a = 0.05. 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 females than expected in the Independent category. (d) Given p-value is 0.002, 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.

Answer 1

using minitab>stat>tables >chi square

we have

Chi-Square Test for Association: data, Worksheet columns

Rows: data Columns: Worksheet columns

Democrat Republican Independent Other All

Female 61 39 19 3 122
54.61 33.11 29.63 4.65
0.865 1.023 -1.953 -0.764
1.797 1.851 -3.467 -1.204
0.748 1.046 3.813 0.584

Male 33 18 32 5 88
39.39 23.89 21.37 3.35
-1.018 -1.204 2.299 0.900
-1.797 -1.851 3.467 1.204
1.037 1.450 5.286 0.810

All 94 57 51 8 210

Cell Contents: Count
Expected count
Standardized residual
Adjusted residual
Contribution to Chi-square

Pearson Chi-Square = 14.773, DF = 3, P-Value = 0.002
Likelihood Ratio Chi-Square = 14.717, DF = 3, P-Value = 0.002

a ) degree of freedom is 3

b ) -1.953

c ) fewer

d ) option b is true