Let's break down the information given in the table:

Part a:

To answer the question, we need to follow these steps:

1. How many subjects did the test find to be lying?

This refers to the number of subjects the polygraph test indicated were lying, which is the sum of the values in the first row ("Polygraph test indicated that the subject lied").

• Number of subjects the test found to be lying = 15 + 47 = 62

2. Of those, how many were actually lying and how many were telling the truth?

• Actually lying: This is the number of subjects who both lied and the polygraph test correctly indicated they lied. From the table, this number is 47.

• Telling the truth: This is the number of subjects who did not lie but the polygraph test incorrectly indicated they lied. From the table, this number is 15.

3. What percentage of those who were found to be lying were not actually lying?

To find this percentage:

• First, calculate the number of subjects who were found to be lying but were not actually lying, which is 15 (from the table).
• Then, divide that number by the total number of subjects who were found to be lying (62) and multiply by 100.

$\text{Percentage} = \left( \frac{15}{62} \right) \times 100 \approx 24\%$

Final Answers:

• There were 62 subjects that were found to be lying.
• Of those, 47 were actually lying and 15 were telling the truth.
• The percentage of those who were found to be lying but were not actually lying was approximately 24%.

Let me know if you need further details or clarifications!

5 Related Questions:

1. What is the formula for calculating the sensitivity and specificity of a test?
2. How does the false positive rate impact the results of a polygraph test?
3. What other types of errors can occur in diagnostic tests like polygraphs?
4. How can you calculate the accuracy of the polygraph test based on this table?
5. What is the importance of having a large sample size in polygraph experiments?

Tip:

When working with confusion matrices (like this table), it’s useful to calculate metrics like accuracy, precision, recall, and F1 score to assess the performance of the test more comprehensively.