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_Not_Lie   Lied
Polygraph_indicated_lie   7   44
Polygraph_indicated_no_lie   29   8

Determine the null and alternative hypotheses.

A.

Upper H 0H0​:

Polygraph testing is not accurate.

Upper H 1H1​:

Polygraph testing is accurate.

B.

Upper H 0H0​:

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

Upper H 1H1​:

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

C.

Upper H 0H0​:

Polygraph testing is accurate.

Upper H 1H1​:

Polygraph testing is not accurate.

D.

Upper H 0H0​:

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

Upper H 1H1​:

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

Determine the test statistic.

chi squaredχ2equals=nothing

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

Determine the​ P-value of the test statistic.

​P-valueequals=nothing

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

Do the results suggest that polygraphs are effective in distinguishing between truth and​ lies?

A.

There isThere is

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

B.

There is notThere is not

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

C.

There is notThere is not

sufficient evidence to warrant rejection of the claim that polygraph testing is​ 95% accurate.

D.

There isThere is

sufficient evidence to warrant rejection of the claim that polygraph testing is​ 95% accurate.

Click to select your answer(s).

Answer 1

B.

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.

χ2 = 37.079

Determine the​ P-value of the test statistic.

​P-value = 0.0000

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

A

There is

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