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?

Did the Subject Actually​ Lie?
	No​ (Did Not​ Lie)		Yes​ (Lied)
Polygraph test indicated that the subject lied.	13		20
Polygraph test indicated that the subject did not lie.	13		7

χ2equals=

P-value=

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.

Answer 1

Applying chi square test of independence:

Observed		column 1	column 2	Total
	row 1	13	20	33
	row 2	13	7	20
	total	26	27	53
Expected	Ei=row total*column total/grand total	column 1	column 2	Total
	row 1	16.1900	16.8113	33
	row 2	9.8113	10.1887	20
	total	26	27	53
chi square    χ2	=(Oi-Ei)2/Ei	column 1	column 2	Total
	row 1	0.6285	0.6048	1.2334
	row 2	1.0363	0.9979	2.0343
	total	1.6649	1.6027	3.2676
test statistic X2 =3.268 (please try 3.27 if required to 2 decimals)
p value =0.0707	(please try 0.071 if required to 3 decimals)

A.There is not sufficient evidence to warrant rejection of the claim that whether a subject lies is independent of the polygraph test indication