(a) Describe the ?x?2??? test for independence of attributes, stating clearly the conditions for its validity.
(b) The table below includes results from polygraph (lie detector) experiments conducted by researchers. In each case, it was known if the subject lied or did not lie, so the table indicates when the polygraph test was correct. Use ?x?2???- test for 0.05 significance level to test the claim that whether a subject lies is independent of the polygraph test indication. Do the results suggest that polygraphs are effective in distinguishing between truth and lies?
Did the subject actually lie?
No(Did not lie) Yes (Lied)
Polygarph test indicated that the subject lied 15 42
Polygarph test indicated that the subject did not lie 32 9