Question

The table below includes results from polygraph​ (lie detector) experiments conducted by researchers. In each​ case, it was known if the subjected lied or did not​ lie, so the table indicates when the polygraph test was correct. Use a 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? Determine the null and alternative hypotheses. A. Ho​: Polygraph testing is not accurate. H1​: Polygraph testing is accurate. B. Ho​: Whether a subject lies is independent of the polygraph test indication. H1​: Whether a subject lies is not independent of the polygraph test indication. C. Ho​: Polygraph testing is accurate. H1​: Polygraph testing is not accurate. D. Ho​: Whether a subject lies is not independent of the polygraph test indication. H1​: Whether a subject lies is independent of the polygraph test indication. Determine the test statistic. χ2 = ____________​ (Round to three decimal places as​ needed.) Determine the​ P-value of the test statistic. ​P-value = ____________ ​(Round to four decimal places as​ needed.) Do the results suggest that polygraphs are effective in distinguishing between truth and​ lies? A. There is not sufficient evidence to warrant rejection of the claim that whether a subject lies is independent of the polygraph test indication. B. There is sufficient evidence to warrant rejection of the claim that whether a subject lies is independent of the polygraph test indication. C. There is not sufficient evidence to warrant rejection of the claim that polygraph testing is​ 95% accurate. D. There is sufficient evidence to warrant rejection of the claim that polygraph testing is​ 95% accurate. ___________________________________________________________________________ Did the Subject Actually​ Lie? No​ (Did Not​ Lie) Yes​ (Lied) Polygraph test indicated that the subject lied. 20 41 Polygraph test indicated that the subject did not lie. 22 11

Answer 1

B. Ho​: Whether a subject lies is independent of the polygraph test indication.

H1​: Whether a subject lies is not independent of the polygraph test indication.

Applying chi square test of independence:

Expected	Ei=row total*column total/grand total	Yes	No	Total
	did not lie	27.3	33.7	61
	lied	14.7	18.3	33
	total	42	52	94
chi square    χ2	=(Oi-Ei)2/Ei	Yes	No	Total
	did not lie	1.931	1.560	3.4913
	lied	3.570	2.884	6.4536
	total	5.5014	4.4435	9.9449
test statistic X2=		9.945

p value =

0.0016

from excel: chidist(9.9449,1)

since p value is less than 0.05:

B. There is sufficient evidence to warrant rejection of the claim that whether a subject lies is independent of the polygraph test indication.