Pro-Choice/Pro-Life and Region of the Country The results of a 2013 Gallup poll about people's position on abortion (pro-life or pro-choice) by region in the country are summarized in the contingency table below. East Midwest South West Totals Pro-Life 212 106 176 188 682 Pro-Choice 184 94 231 215 724 Totals 396 200 407 403 1406 Please respond to one of the following questions, using the table above. For whatever question you answer, make sure you show and explain your work. 1. Test whether or not there is a dependent relationship between abortion stance and region of the country. Conduct the test at the 0.10 significance level. a) What is the n? b) What is the df? c) What is the null hypothesis? (Be specific - don't use generic wording.) d) What is the alternate hypothesis? (Again, be specific - don't use generic wording.) e) Calculate the expected frequencies, keeping the data organized in table format. f) Calculate the chi-squared test statistic. Show your work. g) Calculate the p-value. h) Make a decision about whether to reject or fail to reject the null hypothesis by comparing the p-value to the criterion level. Again, make sure you avoid using generic wording. What specific null hypothesis are we rejecting or failing to reject? i) Make a concluding statement about whether the variables are dependent or not. Be specific: Is the probability that a person is pro-choice or pro-life dependent on the region of the country where he/she lives or not? 2. Test whether or not there is a dependent relationship between abortion stance and region of the country. Conduct the test at the 0.05 significance level. a) What is the n? b) What is the df? c) What is the null hypothesis? (Be specific - don't use generic wording.) d) What is the alternate hypothesis? (Again, be specific - don't use generic wording.) e) Calculate the expected frequencies, keeping the data organized in table format. f) Calculate the chi-squared test statistic. Show your work. g) Calculate the p-value. h) Make a decision about whether to reject or fail to reject the null hypothesis by comparing the p-value to the criterion level. Again, make sure you avoid using generic wording. What specific null hypothesis are we rejecting or failing to reject? i) Make a concluding statement about whether the variables are dependent or not. Be specific: Is the probability that a person is pro-choice or pro-life dependent on the region of the country where he/she lives or not? 3. Test whether or not there is a dependent relationship between abortion stance and region of the country. Conduct the test at the 0.01 significance level. a) What is the n? b) What is the df? c) What is the null hypothesis? (Be specific - don't use generic wording.) d) What is the alternate hypothesis? (Again, be specific - don't use generic wording.) e) Calculate the expected frequencies, keeping the data organized in table format. f) Calculate the chi-squared test statistic. Show your work. g) Calculate the p-value. h) Make a decision about whether to reject or fail to reject the null hypothesis by comparing the p-value to the criterion level. Again, make sure you avoid using generic wording. What specific null hypothesis are we rejecting or failing to reject? i) Make a concluding statement about whether the variables are dependent or not. Be specific: Is the probability that a person is pro-choice or pro-life dependent on the region of the country where he/she lives or not? Chi-Square Test Observed Frequencies Column variable East Midwest South 212 106 176 184 94 231 Total 396 200 407 Calculations West 188 215 403 Total 682 724 1406 Expected Frequencies Column variable 0 East Midwest South West Pro-Life 192.0853 97.0128 197.4211 195.4808 Pro-Choice 203.9147 102.9872 209.5789 207.5192 Total 396 200 407 403 Total 682 724 1406 Pro-Life Pro-Choice Data Level of Significance Number of Rows Number of Columns Degrees of Freedom 0.1 2 4 3 Results Critical Value 6.251389 Chi-Square Test Statistic 10.69608 p-Value 0.013488 Reject the null hypothesis Expected frequency assumption is met. fo-fe 19.91465 8.987198 -19.91465 -8.987198 (fo-fe)^2/fe 2.064673 0.832568 1.944899 0.78427 fo-fe -21.42105 -7.480797 21.42105 7.480797 (fo-fe)^2/fe 2.324278 0.28628 2.189445 0.269673 Chi-Square Test Observed Frequencies Column variable East Midwest South 212 106 176 184 94 231 Total 396 200 407 Calculations West 188 215 403 Total 682 724 1406 Expected Frequencies Column variable 0 East Midwest South West Pro-Life 192.0853 97.0128 197.4211 195.4808 Pro-Choice 203.9147 102.9872 209.5789 207.5192 Total 396 200 407 403 Total 682 724 1406 Pro-Life Pro-Choice Data Level of Significance Number of Rows Number of Columns Degrees of Freedom 0.05 2 4 3 Results Critical Value 7.814728 Chi-Square Test Statistic 10.69608 p-Value 0.013488 Reject the null hypothesis Expected frequency assumption is met. fo-fe 19.91465 8.987198 -19.91465 -8.987198 (fo-fe)^2/fe 2.064673 0.832568 1.944899 0.78427 fo-fe -21.42105 -7.480797 21.42105 7.480797 (fo-fe)^2/fe 2.324278 0.28628 2.189445 0.269673 Chi-Square Test Observed Frequencies Column variable East Midwest South 212 106 176 184 94 231 Total 396 200 407 Calculations West 188 215 403 Total 682 724 1406 Expected Frequencies Column variable 0 East Midwest South West Pro-Life 192.0853 97.0128 197.4211 195.4808 Pro-Choice 203.9147 102.9872 209.5789 207.5192 Total 396 200 407 403 Total 682 724 1406 Pro-Life Pro-Choice Data Level of Significance Number of Rows Number of Columns Degrees of Freedom 0.01 2 4 3 Results Critical Value 11.34487 Chi-Square Test Statistic 10.69608 p-Value 0.013488 Do not reject the null hypothesis Expected frequency assumption is met. fo-fe 19.91465 8.987198 -19.91465 -8.987198 (fo-fe)^2/fe 2.064673 0.832568 1.944899 0.78427 fo-fe -21.42105 -7.480797 21.42105 7.480797 (fo-fe)^2/fe 2.324278 0.28628 2.189445 0.269673 Chi-Square Test Observed Frequencies Column variable East Midwest South 212 106 176 184 94 231 Total 396 200 407 Calculations West 188 215 403 Total 682 724 1406 Expected Frequencies Column variable 0 East Midwest South West Pro-Life 192.0853 97.0128 197.4211 195.4808 Pro-Choice 203.9147 102.9872 209.5789 207.5192 Total 396 200 407 403 Total 682 724 1406 Pro-Life Pro-Choice Data Level of Significance Number of Rows Number of Columns Degrees of Freedom 0.1 2 4 3 Results Critical Value 6.251389 Chi-Square Test Statistic 10.69608 p-Value 0.013488 Reject the null hypothesis Expected frequency assumption is met. fo-fe 19.91465 8.987198 -19.91465 -8.987198 (fo-fe)^2/fe 2.064673 0.832568 1.944899 0.78427 fo-fe -21.42105 -7.480797 21.42105 7.480797 (fo-fe)^2/fe 2.324278 0.28628 2.189445 0.269673 Chi-Square Test Observed Frequencies Column variable East Midwest South 212 106 176 184 94 231 Total 396 200 407 Calculations West 188 215 403 Total 682 724 1406 Expected Frequencies Column variable 0 East Midwest South West Pro-Life 192.0853 97.0128 197.4211 195.4808 Pro-Choice 203.9147 102.9872 209.5789 207.5192 Total 396 200 407 403 Total 682 724 1406 Pro-Life Pro-Choice Data Level of Significance Number of Rows Number of Columns Degrees of Freedom 0.05 2 4 3 Results Critical Value 7.814728 Chi-Square Test Statistic 10.69608 p-Value 0.013488 Reject the null hypothesis Expected frequency assumption is met. fo-fe 19.91465 8.987198 -19.91465 -8.987198 (fo-fe)^2/fe 2.064673 0.832568 1.944899 0.78427 fo-fe -21.42105 -7.480797 21.42105 7.480797 (fo-fe)^2/fe 2.324278 0.28628 2.189445 0.269673 Chi-Square Test Observed Frequencies Column variable East Midwest South 212 106 176 184 94 231 Total 396 200 407 Calculations West 188 215 403 Total 682 724 1406 Expected Frequencies Column variable 0 East Midwest South West Pro-Life 192.0853 97.0128 197.4211 195.4808 Pro-Choice 203.9147 102.9872 209.5789 207.5192 Total 396 200 407 403 Total 682 724 1406 Pro-Life Pro-Choice Data Level of Significance Number of Rows Number of Columns Degrees of Freedom 0.01 2 4 3 Results Critical Value 11.34487 Chi-Square Test Statistic 10.69608 p-Value 0.013488 Do not reject the null hypothesis Expected frequency assumption is met. fo-fe 19.91465 8.987198 -19.91465 -8.987198 (fo-fe)^2/fe 2.064673 0.832568 1.944899 0.78427 fo-fe -21.42105 -7.480797 21.42105 7.480797 (fo-fe)^2/fe 2.324278 0.28628 2.189445 0.269673