# 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 â€œMetabolite Aâ€ in the serum. The other test (Test B) measures a different metabolite, â€œMetabolite Bâ€ 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 â€œgold standardâ€ 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 â€“ 1.99                                                 25                                22                                3

2.0 â€“ 3.99                                273                              201                              72

4.0 â€“ 5.99                                584                              572                              12

6.0 â€“ 7.99                                538                              529                                9

8.0 â€“ 9.99                                175                              170                                5

>10.0                                         14                                14                                0

Urine level (metabolite B)

(ng/ml)

0 â€“ 2.99                                                 30                                  5                              25

3.0 â€“ 5.99                                245                                46                                         199

6.0 â€“ 8.99                                423                              400                              23

9.0 â€“ 11.99                              628                              620                                8

12.0 â€“ 14.99                            175                              169                                6

15.0 â€“ 17.99                              99                                95                                4

>18.0                                           9                                  9                                0

a)      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 â€œnegativeâ€ and values of 4.0 mg / ml or greater are considered â€œpositiveâ€).

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 â€œnegativeâ€ and values of 6.0 ng / ml or greater are considered â€œpositiveâ€).

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?

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