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 0.01 significance level.

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

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

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

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

2 =  

(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.

Republican Independent Democrat Totals For Checks   287   68     310     665   Against Checks   81   12     42     135   Totals   368     80     352     800  

Explanation / Answer

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

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

(b)

Expected frequency

For checks - Republican = Total republican * Total For checks/ Totalpopulation = 368 * 665/ 800 = 305.9

similarly all values are given in the expected table

here chi-square X2  = (O - E)2/E

2 = 13.25

(c) p - value= 0/001325

(d) Here p-value is less than 0.05 significance level. reject H0

(e)

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

Option B is correct.

Republican Independent Democrat Totals For Checks   287   68     310     665   Against Checks   81   12     42     135   Totals   368     80     352     800  

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