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? State the null and alternate hypothesis, test statistic, p-value and conclusion.

_	Did_Not_Lie	Lied
Polygraph_indicated_lie	15	50
Polygraph_indicated_no_lie	21	12

Answer 1

Claim: polygraphs are effective in distinguishing between truth and? lies

The null and alternative hypothesis is

H0: polygraphs are not effective in distinguishing between truth and? lies.

H1: polygraphs are effective in distinguishing between truth and? lies.

Level of significance = 0.05

Test statistic is

O: Observed frequency
E: Expected frequency.

E = ( Row total* Column total) / Grand total

	Did Not lie	Lied	Total
Polygraph indicated lie	15	50	65
Polygraph indicated no lie	21	12	33
Total	36	62	98

O	E	(O-E)	(O-E)^2	(O-E)^2/E
15	23.87755	-8.87755	78.81091	3.300627943
50	41.12245	8.877551	78.81091	1.916493645
21	12.12245	8.877551	78.81091	6.501236858
12	20.87755	-8.87755	78.81091	3.774911724
			Total	15.493

Degrees of freedom = (r-1)*(c-1) = (2-1)*(2-1) = 1*1 = 1

P-value = P() = 0.000083

P-value < 0.05 we reject null hypothesis.

Conclusion:

polygraphs are effective in distinguishing between truth and? lies.