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: O_i's

	Republican	Independent	Democrat	Totals
For Checks	275	68	331	674
Against Checks	69	12	45	126
Totals	344	80	376	800

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

(a) What is the null hypothesis for this test?

H₀: Party affiliation and opinion on expanded background checks are dependent variables.H₀: Party affiliation and opinion on expanded background checks are independent variables.     

(b) What is the value of the test statistic? Round to 3 decimal places unless your software automatically rounds to 2 decimal places.

χ²

=

(c) Use software to get the P-value of the test statistic. Round to 4 decimal places unless your software automatically rounds to 3 decimal places.
P-value =

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

reject H₀fail to reject H₀    

(e) Choose the appropriate concluding statement.

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

Answer 1

The statistical software output for this problem is :

.H₀: Party affiliation and opinion on expanded background checks are independent variables.

Test statistics = 8.898

P-value = 0.0117

reject H₀

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