To test the claim that whether a subject lies or does not lie is independent of the polygraph test indication, we can use the chi-squared test for independence.
First, we need to calculate the expected frequencies for each cell in the table under the assumption of independence. This is done by multiplying the row total by the column total and dividing by the grand total.
Expected frequency for "Polygraph test indicated that the subject lied" and "Lied": E1 = (42+15)(42+9)/(42+15+32+9) = 27.014
Expected frequency for "Polygraph test indicated that the subject lied" and "Did not lie": E2 = (42+15)(15+32)/(42+15+32+9) = 29.986
Expected frequency for "Polygraph test indicated that the subject did not lie" and "Lied": E3 = (9+32)(42+9)/(42+15+32+9) = 23.986
Expected frequency for "Polygraph test indicated that the subject did not lie" and "Did not lie": E4 = (9+32)(15+32)/(42+15+32+9) = 17.014
Next, we calculate the test statistic:
Chi-squared = Σ((O-E)^2/E), where O is the observed frequency and E is the expected frequency.
Chi-squared = ((42-27.014)^2/27.014) + ((15-29.986)^2/29.986) + ((9-23.986)^2/23.986) + ((32-17.014)^2/17.014) = 25.571
Therefore, the test statistic needed to test the claim is 25.571. The answer is A. 25.571.
The table includes results from polygraph experiments. In each case, it was known if the subject lied or did not lie, so the table indicates when the polygraph test was correct. Find the test statistic needed to test the claim that whether a subject lies or does not lie is independent of the polygraph test indication.
Polygraph test indicated that the subject lied:
Lied: 42
Did not lie: 15
Polygraph test indicated that the subject did not lie:
Lied: 9
Did not lie: 32
A. 25.571
B. 3.841
C. 10.147
D. 27.337
1 answer
3 answers