Question

A.

x 11.2.5-T Is Question Help 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? FH: Click the icon to view the table. Determine the * More Info O A. Ho:P H:P Did the Subject Actually Lie? No (Did Not Lie) Yes (Lied) Polygraph test indicated that 17 24 the subject lied. Polygraph test indicated that 18 10 the subject did not lie. OD. Ho:P H:P Print Done Determine the = (Round to three decimal places as needed.) How Enter your answer in the answer box and then click Check Answer. 2 parts 2 remaining Clear All Check Answer

Determine the Test Statistic

x^{2=______(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 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.

B.

Determine the Test Statistic

x^{2=______(Round to three decimal places as needed)}

Determine the P-Value of the test statistic

P-value=_____(Round to four decimal places as needed)

Is there sufficient evidence to support the claim that results from the test are discriminatory?

(a) there is not sufficient evidence to support the claim that results are discriminatory. (

b) there is sufficient evidence to support the claim that the results are discriminatory.

(c) there is not sufficient evidence to reject the claim that a white candidate is more likely to pass the test than a minority candidate.

(d) there is sufficient evidence to reject the claim that a white candidate is more likely to pass the test than a minority candidate.

Answer 1

SOLUTION:

From given data,

Add up rows and columns:

(O)	No (Did Not Lie)	Yes(Lied)	Total
Polygraph test indicated that the subject lied.	17	24	41
Polygraph test indicated that the subject did not lie.	18	10	28
Total	35	34	69

Calculate "Expected Value" for each entry:

Multiply each row total by each column total and divide by the overall total:

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

(E)	No (Did Not Lie)	Yes(Lied)
Polygraph test indicated that the subject lied.	35*41/ 69 = 20.7971	34*41/ 69 = 20.2029
Polygraph test indicated that the subject did not lie	35*28 / 69 = 14.2029	34*28/ 69= 13.7971

Subtract expected from actual, square it, then divide by expected:

$\chi ^{2}$ =

ΣΙΟ-ΕΕ

	No (Did Not Lie)	Yes(Lied)
Polygraph test indicated that the subject lied.	(17-20.7971)2 / 20.7971 =0.693268	(24-20.2029)2 / 20.2029 =0.713658
Polygraph test indicated that the subject did not lie	(18-14.2029)2 / 14.2029 =1.015143	(10-13.7971)2 / 13.7971 = 1.044999

Determine the Test Statistic

Now add up those values:

$\chi ^{2}$ =   = 0.693268+0.713658+1.015143+1.044999 = 3.467068

ΣΙΟ-ΕΕ

Chi-Square = $\chi ^{2}$ = 3.467 (Round to three decimal places as needed)

From Chi-Square to p

Calculate Degrees of Freedom

= (rows − 1) $\times$ (columns − 1)

DF = (2 − 1)(2 − 1) = 1×1 = 1

Critical value :

Critical value at  $\alpha$ = 0.05 with   DF = 1

= 3.841

Хо.05-

P- value

P- value at  $\chi ^{2}$ = 3.467 with   DF = 1

P- value =0.0500136

approx , P- value = 0.0500 (Round to four decimal places as needed)

Since P- value is greater than critical value,

we reject null hypothesis. At 5% level , there is sufficient evidence.

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

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