The table below includes results from polygraph (lie detector) experiments condu
ID: 3135041 • Letter: T
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 lie?
Table:
Did the subject Actually Lie?
No (Did not Lie) Yes (lied)
Polygraph test indicated that the subject lied 15 37
Polygraph test indicated that the subject did not lie 7 10
** I'm having a tough time inputting the values of the table here. The data is as follows:
For the first polygraph test that indicated that the subject lied, it was found that 15 did not lie, and 37 lied.
For the polygraph test that indicated that the subject did not lie, it was found that 7 did not lie and 10 did.
Determine the test statistic x^2= (round to three decimal places)
Which of the following P-value range is inappropriate?
a. P-value < 0.01
b. 0.01 < p-value < 0.05
c. 0.05 < p-value < 0.10
d. P-value > 0.10
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 polygraph testing is 95% accurate.
b. There is 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.
Explanation / Answer
a)
Doing an Expected Value Chart,
16.57971014 35.42028986
5.420289855 11.57971014
Using chi^2 = Sum[(O - E)^2/E],
chi^2 = 0.896869557 [ANSWER]
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b)
With df = (a - 1)(b - 1), where a and b are the number of categories of each variable,
a = 2
b = 2
df = 1
Hence, the p value is
P > 0.10 [ANSWER, D]
[I wonder why he says "inappropriate" though. In fact, this is the appropriate choice.]
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C)
As P > 0.10 (big P value), we do not reject the null hypothesis.
OPTION D: d. There is not sufficient evidence to warrant rejection of the claim that whether a subject lies is independent of the polygraph test indication.
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