Imagine that the internal revenue service has developed an automated screening tool that examines all income tax returns and predicts whether or not the return contains fraudulent information. The IRS is trying to decide whether to deploy the tool nationally and use it to examine all tax returns. To inform its decision, the IRS examines a collection of 800 returns to be fraudulent and observes that the automated tool correctly identifies 600 of these as fraudulent. The IRS studies a collection of 1,200 returns known to be error - free and observes that the automated tool flags 1,100 as non-fraudulent. IRS believes that 10 percent all returns contain fraudulent information.

Use the bayes theorem to provide the IRS with the information it needs to decide whether to deploy the new tool nationally. Build a model that lets vary all these input data.

1. Compute the sensitivity and specificity of the automated tool. Display the result with a standard 2x2 table for assessing the accuracy of a testing instrument