Support of Background Checks by Political Party: In April of 2013, the U.S. Sena

Question

Support of Background Checks by Political Party: In April of 2013, the U.S. Senate did not pass a bill to expand background checks to all gun sales despite popular approval of the idea. Gallup conducted a poll on this issue with the question: Would you vote for or against a law to require background checks for all gun sales?. The results by political affiliation are summarized in the contingency table below.

Observed Frequencies: Oi's

The Test: Test for a dependent relationship between party affiliation and opinion on expanded background checks. Conduct this test at the 0.05significance level.

(a) What is the test statistic? Round your answer to 3 decimal places.

2

=  

(b) What is the conclusion regarding the null hypothesis?

reject H0fail to reject H0    

(c) Choose the appropriate concluding statement.

We have proven that opinion on expanded background checks and political affiliation are independent.The evidence suggests that there is a dependent relationship between opinion on expanded background checks and party affiliation.     There is not enough evidence to conclude that opinion on expanded background checks and political affiliation are dependent.

  Republican     Independent     Democrat     Totals   For Checks     284   68     331     683   Against Checks     76   12     29     117   Totals     360     80     360     800  

Explanation / Answer

applying chi square test of independence on above data:

from above  2 =24.582

b) as p value for above =0.0000. As p value is less then 0.05 level therefore

reject H0

c)

The evidence suggests that there is a dependent relationship between opinion on expanded background checks and party affiliation.

Observed O republic independent democrat Total for checks 284 68 331 683 against checks 76 12 29 117 Total 360 80 360 800 Expected E=rowtotal*column total/grand total republic independent democrat Total for checks 307.35 68.30 307.35 683 against checks 52.65 11.70 52.65 117 Total 360 80 360 800 chi square =(O-E)^2/E republic independent democrat Total for checks 1.7739 0.0013 1.8198 3.595 against checks 10.356 0.008 10.623 20.987 Total 12.130 0.009 12.443 24.582

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