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	297	75	296	668
Against Checks	79	13	40	132
Totals	376	88	336	800

The Test: Test for a dependent relationship between party affiliation and opinion on expanded background checks. Conduct this test at the 0.01 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 H₀

fail 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 statistic software output for this problem is:

(a)

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

(b)

Chi square = 10.893

(c)

P-value = 0.0043

(d)

reject H₀

Option a)