Accuracy of Polygraph Tests - The data in the table belowsummarize results from
ID: 2914397 • Letter: A
Question
Accuracy of Polygraph Tests - The data in the table belowsummarize results from tests of the accuracy of polygraphs. Use a 0.05 significance level to test the claim that whether thesubject lies in independent of polygraph indication. What dothe results suggest about the effectiveness of polygraphs? ------------------------------------Polygraph IndictaedTruth-----Polygraph Indicated Lie Subject actually told thetruth------------------65-------------------------15-------------- Subject actually told alie-----------------------3--------------------------17-------------- Accuracy of Polygraph Tests - The data in the table belowsummarize results from tests of the accuracy of polygraphs. Use a 0.05 significance level to test the claim that whether thesubject lies in independent of polygraph indication. What dothe results suggest about the effectiveness of polygraphs? ------------------------------------Polygraph IndictaedTruth-----Polygraph Indicated Lie Subject actually told thetruth------------------65-------------------------15-------------- Subject actually told alie-----------------------3--------------------------17--------------Explanation / Answer
Null Hypothesis: the subject lies inindependent of polygraph indication Alternative hypothesis: the subject lies in notindependent of polygraph indication Consider the following table Truth Lie Total actually truth 65 15 80 actually lie 3 17 20 Total 68 32 100 Truth Lie actually truth 54.4 25.6 actually lie 13.6 6.4 Oi Ei (Oi-Ei)^2 (Oi-Ei)^2/Ei 65 54.4 112.36 2.065441 3 13.6 112.36 8.261765 15 25.6 112.36 4.389063 17 6.4 112.36 17.55625 Total 32.27252 Truth Lie Total actually truth 65 15 80 actually lie 3 17 20 Total 68 32 100 Truth Lie actually truth 54.4 25.6 actually lie 13.6 6.4 Oi Ei (Oi-Ei)^2 (Oi-Ei)^2/Ei 65 54.4 112.36 2.065441 3 13.6 112.36 8.261765 15 25.6 112.36 4.389063 17 6.4 112.36 17.55625 Total 32.27252The critical value of chi-square at (2-1)X(2-1)dfand at 0.05, the level of significance is 3.841 Since the calculated value is greater than thtecritical value of chi-square so we reject the null hypothesis andconclude that the subject lies in not independent ofpolygraph indication Truth Lie Total actually truth 65 15 80 actually lie 3 17 20 Total 68 32 100 Truth Lie actually truth 54.4 25.6 actually lie 13.6 6.4 Oi Ei (Oi-Ei)^2 (Oi-Ei)^2/Ei 65 54.4 112.36 2.065441 3 13.6 112.36 8.261765 15 25.6 112.36 4.389063 17 6.4 112.36 17.55625 Total 32.27252