2 questions in statistic: help wanted

# 2 questions in statistic: help wanted

1.What are the odds of rolling a seven using two, standard, fair dice? 2. Two new tests have been developed to diagnose Condition Z. One test (Test A) measures a metabolite Metabolite A in the serum. The other test (Test B) measures a different metabolite, Metabolite B in the urine. After appropriate preliminary testing, human trials are conducted. Following informed consent, the two tests were run on a group of patients with each patient getting both tests, as well as the gold standard test for diagnosing Condition Z. The following data were obtained:Important!!!! Since some answers depend on the results you obtained in previous sections of the problem, it is important for you that you show *all* work, since I will give partial credit if your analysis and set up are correct, even if your numerical result is incorrect.Serum level (metabolite A) # of patients Disease positive Disease negative(mg / ml) (by gold standard) (by gold standard)0 1.99 25 22 32.0 3.99 273 201 72 4.0 5.99 584 572 126.0 7.99 538 529 98.0 9.99 175 170 5>10.0 14 14 0Urine level (metabolite B)(ng/ml)0 2.99 30 5 253.0 5.99 245 46 199 6.0 8.99 423 400 239.0 11.99 628 620 812.0 14.99 175 169 615.0 17.99 99 95 4>18.0 9 9 0a) For test A, a cutoff value of 4.0 mg / ml of metabolite A is chosen as the boundary between a negative and a positive test result (i.e., values below 4.0 mg / ml are considered negative and values of 4.0 mg / ml or greater are considered positive).For test B, a cutoff value of 6.0 ng / ml for metabolite B is chosen as the boundary between a negative and a positive test result (i.e., values below 6.0 ng / ml are considered negative and values of 6.0 ng / ml or greater are considered positive).i. Create a fully labeled 2 x 2 table for test A ii. Create a fully labeled 2 x 2 table for test B iii. Which test is the more sensitive at diagnosing Condition Z? iv. Which test is the more specific at diagnosing Condition Z? b) What is the post-test probability of disease being present in a patient with a positive test result for test A if the pre-test probability of Condition Z is 8%, and the cutoff value of 4.0 mg/ml is chosen?