Medicare reimbursement regulations require no more than a 6% error rate in invoi
ID: 3043257 • Letter: M
Question
Medicare reimbursement regulations require no more than a 6% error rate in invoice coding from a service provider. You draw a random same of 60 invoices and, upon audit, find that there are 6 errors in the 60 invoices sampled. If the true billing error rate for this service provider were no higher than 6%, what is the probability of having observed at least 6 errors in your sample? Suppose, on the basis of your answer to the immediately previous question, you assert that this service provider does not meet the Medicare standard of no more than a 6% error rate. What is the false positive probability of your assertion?
Explanation / Answer
Here,
number of invoices = 60
error rate = 6%
expected number of error = 60 * 6% = 3.6
number of errors found = 6
Here the distribution is binomial distribution.
so as we have to calculate, if X is the number of errors out of 60 invoices.
Pr(X>= 6) = BINOMIAL (X >= 6 ; 60 ; 0.06)
we will not use normal approximation as p - value is very less and the curve shall not be symmetric. So, from BINOMIAL TABLE for n = 60 and p = 0.06
Pr(X>= 6) = BINOMIAL (X >= 6 ; 60 ; 0.06) = 1- BINOMIAL (X <= 5; 60 ; 0.06) = 1 - 0.8502 = 0.1498 > 0.05
as we can assert that this service provider meet the Medicare standard of no more than a 6% error rate.
Here false positive probability is 0.15 as there are 0.15 probability that we will assume that we will assert that servive provider doesnot meet the medicare standard