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	299	671
Against Checks	79	13	37	129
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 0.05 significance level.

(a) What is the null hypothesis for this test?
1. H₀: Party affiliation and opinion on expanded background checks are independent variables.
2. 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?
1. reject H_0
2. fail to reject H₀   

(e) Choose the appropriate concluding statement.
1. We have proven that opinion on expanded background checks and party affiliation are independent.
2. The evidence suggests that there is a dependent relationship between party affiliation and opinion on expanded background checks.    
3. There is not enough evidence to conclude that party affiliation and opinion on expanded background checks are dependent.

Answer 1

Answer Date: 13/04/2018 To test the hypothesis is that there is a dependent relationship between party affiliation and opinion on expanded background checks at 5% level of significance. a) The null and alternative hypothesis is, The null hypothesis is that there is no dependent relationship between party affiliation and opinion on expanded background checks The alternative hypothesis is that there is a dependent relationship between party affiliation and opinion on expanded background checks b) The chi-square test statistic of independence is, By using MINITAB software, find chi-square with help of following steps 1) Import the data. 2) Select Chi-Square Test (Table in Worksheet) from Tables in Stat menu 3) Select Columns containing the table.

4) Click Ok Chi-Square Test: Republican, Independent, Democrat Expected counts are printed below observed counts Chi-Square contributions are printed below expected counts Republican Independent Democrat Total 671 297 315.37 1.070 75 73.81 0.019 299 281.82 1.047 129 79 60.63 5.566 13 14.19 0.100 37 54.18 5.448 2 Total 376 336 800 Chi-Sq-13.250, DF2, P-Value0.001 From the MINITAB output, the chi-square test statistic for goodness-of-fit test is 13.250 c) Thep-value is,

From the MINITAB output in part (b), the chi-square test p-value is 0.001 The p-value is | 0.001- d) Decision The conclusion is that the significant p-value is less than 0.05 which is 0.001, so the null hypothesis is rejected at 5% level of significance. e) There is sufficient evidence to indicate that there is a dependent relationship between party affiliation and opinion on expanded background checks. The result is statistically significant The answer is2