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?

. Determine the null and alternative hypotheses.

A. Upper H0 : 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=\\(Round to three decimal places as needed.)

Determine the P-value of the test statistic. P-valueequals= (Round to four decimal places as needed.)

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

A. There is notThere is not sufficient evidence to warrant rejection of the claim that polygraph testing is 95% accurate. B. There isThere is 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 whether a subject lies is independent of the polygraph test indication. D. There isThere is sufficient evidence to warrant rejection of the claim that polygraph testing is 95% accurate.

Did the Subject Actually​ Lie?
	No​ (Did Not​ Lie)		Yes​ (Lied)
Polygraph test indicated that the subject lied.	18		24
Polygraph test indicated that the subject did not lie.	24		15

Answer 1

Solution:-

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

(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.

Formulate an analysis plan. For this analysis, the significance level is 0.05. Using sample data, we will conduct a chi-square test for independence.

Analyze sample data. Applying the chi-square test for independence to sample data, we compute the degrees of freedom, the expected frequency counts, and the chi-square test statistic. Based on the chi-square statistic and the degrees of freedom, we determine the P-value.

DF = (r - 1) * (c - 1) = (2 - 1) * (2 - 1)
D.F = 1
Er,c = (nr * nc) / n

Χ² = 2.827

where DF is the degrees of freedom.

The P-value is the probability that a chi-square statistic having 1 degrees of freedom is more extreme than 2.83.

We use the Chi-Square Distribution Calculator to find P(Χ² > 2.83) = 0.0927

Interpret results. Since the P-value (0.0927) is greater than the significance level (0.05), we fail to reject null hypothesis.

Thus, we conclude that there is a relationship between gender and voting preference.

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