Questions: Assume the sample is representative of the entire population for a person selected at random, compute the following probabilities. Enter your answer as a fraction. (a) P+ condition present) : this is known as the sensitivity of a test 66/149 (b) P+ condition present) : this is known as the specificity of a test 83/149 (c) P+ condition present) : this is known as the false negative rate 72/149 (d) P+ condition present) : this is known as the false positive rate 40/149 (e) P+ condition present) : this is known as the positive predictive value 66/106 (f) P+ condition present) : this is known as the negative predictive value 83/112 (g) P(condition present and -) : this is 72/149 (h) P(-) : 112/149 (i) P(condition present or +) : this is 106/149

$Assume the sample is representative of the entire population for a person selected at random, compute the following probabilities. Enter your answer as a fraction. (a) P+ condition present) : this is known as the sensitivity of a test 66/149 (b) P+ condition present) : this is known as the specificity of a test 83/149 (c) P+ condition present) : this is known as the false negative rate 72/149 (d) P+ condition present) : this is known as the false positive rate 40/149 (e) P+ condition present) : this is known as the positive predictive value 66/106 (f) P+ condition present) : this is known as the negative predictive value 83/112 (g) P(condition present and -) : this is 72/149 (h) P(-) : 112/149 (i) P(condition present or +) : this is 106/149$

Transcript text: Assume the sample is representative of the entire population for a person selected at random, compute the following probabilities. Enter your answer as a fraction. (a) P+ | condition present) : this is known as the sensitivity of a test 66/149 (b) P+ | condition present) : this is known as the specificity of a test 83/149 (c) P+ | condition present) : this is known as the false negative rate 72/149 (d) P+ | condition present) : this is known as the false positive rate 40/149 (e) P+ | condition present) : this is known as the positive predictive value 66/106 (f) P+ | condition present) : this is known as the negative predictive value 83/112 (g) P(condition present and -) : this is 72/149 (h) P(-) : 112/149 (i) P(condition present or +) : this is 106/149

Solution

Solution Steps

To solve the given probabilities, we need to extract the relevant values from the table and use them to compute the required probabilities. Each probability is a fraction based on the given data.

Solution Approach

Extract the relevant values from the table.
Compute each probability as a fraction using the extracted values.

Step 1: Calculate Sensitivity

The sensitivity of a test, denoted as $ P(+ | \text{condition present}) $, is calculated using the formula:

\[ P(+ | \text{condition present}) = \frac{\text{True Positives}}{\text{Total Condition Present}} = \frac{66}{149} \approx 0.443 \]

Step 2: Calculate Specificity

The specificity of a test, denoted as $ P(+ | \text{condition absent}) $, is calculated using the formula:

\[ P(+ | \text{condition absent}) = \frac{\text{True Negatives}}{\text{Total Condition Absent}} = \frac{83}{149} \approx 0.557 \]

Step 3: Calculate False Negative Rate

The false negative rate, denoted as $ P(- | \text{condition present}) $, is calculated using the formula:

\[ P(- | \text{condition present}) = \frac{\text{False Negatives}}{\text{Total Condition Present}} = \frac{72}{149} \approx 0.483 \]

Final Answer

Sensitivity: $ \boxed{0.443} $
Specificity: $ \boxed{0.557} $
False Negative Rate: $ \boxed{0.483} $

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