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         11   50
Polygraph_indicated_no_lie   17           15

Determine the null and alternative hypotheses.

A.Upper H 0​: Whether a subject lies is independent of the polygraph test indication.

Upper H 1​: Whether a subject lies is not independent of the polygraph test indication.

B.Upper H 0​: Whether a subject lies is not independent of the polygraph test indication.

Upper H 1: Whether a subject lies is independent of the polygraph test indication.

C.Upper H 0​: Polygraph testing is accurate.

Upper H 1​: Polygraph testing is not accurate.

D.Upper H 0​: Polygraph testing is not accurate.

Upper H 1​: Polygraph testing is accurate.

Determine the test statistic.

chi squared=____________

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

B.There is not sufficient evidence to warrant rejection of the claim that polygraph testing is​ 95% accurate.

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

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

Answer 1

Here chi square test of independence will be used.

Hypotheses are:

A.Upper H 0​: Whether a subject lies is independent of the polygraph test indication.

Upper H 1​: Whether a subject lies is not independent of the polygraph test indication.

Following table shows the row total and columns total:

	The subject actually did not lie	The subject actually lie	Total
Polygraph indiactes lie	11	50	61
Polygraph indictaes truth	17	15	32
Total	28	65	93

Expected frequencies will be calculated as follows:

Following table shows the expected frequencies:

	The subject actually did not lie	The subject actually lie	Total
Polygraph indiactes lie	18.366	42.634	61
Polygraph indictaes truth	9.634	22.366	32
Total	28	65	93

Following table shows the calculations for chi square test statistics:

O	E	(O-E)^2/E
11	18.366	2.954260917
17	9.634	5.631924019
50	42.634	1.272645213
15	22.366	2.425912367
Total		12.28474252

The test statistics is

Degree of freedom: df =( number of rows -1)*(number of columns-1) = (2-1)*(2-1)=1

The p-value is : 0.0005

Since p-value is less than 0.05 so we reject the null hypothesis.

Correct option:

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