Let's break this down:

Given:

• The probability that a randomly selected polygraph test subject was not lying is 0.484.
• The probability of a negative test result (where the subject is determined to be "not lying") is 0.441.

We need to check if the result is close by comparing the absolute difference between these two probabilities. The condition given is that they are considered "close" if the absolute difference is less than 0.050.

Step 1: Calculate the absolute difference between the probabilities

$\text{Absolute Difference} = |0.484 - 0.441| = 0.043$

Step 2: Compare the absolute difference to 0.050

Since 0.043 is less than 0.050, we can conclude that the probabilities are close.

Conclusion:

The result is close because there is a 0.043 absolute difference between the probability of a true response (not lying) and the probability of a negative test result.

Would you like further clarification or examples? Here are some related questions to help deepen the understanding:

1. How can the concept of absolute difference be applied to other probability comparisons?
2. What is the importance of rounding probabilities to a specific decimal place in real-world applications like polygraph testing?
3. How do conditional probabilities relate to the interpretation of polygraph test results?
4. In what ways can we improve the accuracy of polygraph tests to minimize differences like these?
5. What does the concept of "close enough" mean in the context of statistical testing?

Tip: When comparing probabilities, always ensure you are using the same number of decimal places for consistency before making conclusions!