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	282	75	320	677
Against Checks	70	13	40	123
Totals	352	88	360	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

Tabulated Statistics: C1, Worksheet columns

Rows: C1   Columns: Worksheet columns

	Republican	Independent	Democrat	All
For Checks	282	75	320	677
	297.88	74.47	304.65
Against Checks	70	13	40	123
	54.12	13.53	55.35
All	352	88	360	800

Cell Contents
      Count
      Expected count

Chi-Square Test

	Chi-Square	DF	P-Value
Pearson	10.561	2	0.005

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

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b) 10.561

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c) P-value = 0.005

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d) Reject Ho

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