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.	1212		3535
Polygraph test indicated that the subject did not lie.	3535		1414

A. H0​: Polygraph testing is accurate. H1​: Polygraph testing is not accurate.

B. H0​: Polygraph testing is not accurate. H1​: Polygraph testing is accurate.

C. H0​: Whether a subject lies is independent of the polygraph test indication. H1​: Whether a subject lies is not independent of the polygraph test indication.

D. H0​: 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.

chi squaredχ2equals=

​(Round to three decimal places as​ needed.)

Determine the​ P-value of the test statistic.

​P-valueequals=

​(Round to four decimal places as​ needed.)

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 polygraph testing is​ 95% accurate.

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 whether a subject lies is independent of the polygraph test indication.

Answer 1

C. H0​: Whether a subject lies is independent of the polygraph test indication.

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

Tabulated Statistics: C1, Worksheet columns

Rows: C1   Columns: Worksheet columns

	NO	Yes	All
Polygraph test indicated that t	12	35	47
	23.01	23.99
	35	14	49
	23.99	25.01
All	47	49	96

Cell Contents
      Count
      Expected count

Chi-Square Test

	Chi-Square	DF	P-Value
Pearson	20.222	1	0.000

==========================================================

P-value = 0.0000

==========================================================

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