To diagnose active tuberculosis (TB) infection, doctors consider patients symptoms and results of lab tests and x-rays. The lab test that can confirm the presence of the bacteria (active TB infection) can take several weeks for results.\ \ Suppose a new rapid sputum test is created to screen for TB bacteria with a turnaround time of 15 minutes. We administer the new sputum test to 2000 patients who present with any of the potential symptoms that overlap with a TB diagnosis. We use a complete work-up and physician diagnosis of TB as the gold standard. Using our new sputum test, 550 patients screen positive for TB. Of those who screen positive, 400 are found to have TB based on the physician work-up. Of those who screen negative for TB, 100 are diagnosed with TB during the physician work-up.\ \ \ 1. Construct a 2x2 table based on the information provided above.\ \ Physician Work-Up Gold Standard\ New Sputum Test TB No TB Total\ Positive 400 150 550\ Negative 100 1350 1450\ Total 500 1500 2000\ \ \ 2. What is the prevalence of TB in this population? Express as a percentage and round to the nearest whole number. \ 25%\ \ 3. Calculate the accuracy of the screening test. Express as a percentage and round to the nearest whole number. \ 88%\ \ 4. What is the sensitivity of the test? Express as a percentage, round to the nearest whole number, and then interpret the sensitivity in words.\ \ \ 5. Calculate the specificity of the test. Express as a percentage, round to the nearest whole number, and then interpret the specificity in words.\ \ \ 6. What is the positive predictive value of this test? Express as a percentage, round to the nearest whole number, and then interpret the PPV in words.\ \ \ 7. What is the negative predictive value of this test? Express as a percentage, round to the nearest whole number, and then interpret the NPV in words.\ \ \ 8. Would you recommend this test? Why or why not?\