# A hypothesis test to determine whether state agencies are paying to much in medicare.

An auditor for a government agency is assigned to the task of evaluating reimbursement for office visits to doctors paid by Medicare. The audit is to be conducted for all Medicare payments in a particular area during a certain month. An audit is conducted on a sample of 75 of the reimbursements with the following results.

Average amount of reimbursement $93.70

Standard deviation of reimbursement $34.55

Number of reimbursements where an

incorrect amount was provided 12

a. At the 0.05 level of significance, is there evidence that the proportion of incorrect reimbursements in the population is greater than 10%? What is the p-value of the test?

b. What is the smallest sample size needed to estimate the mean amount reimbursed to within 50 cents with 90% confidence, if a preliminary study indicates that the sample standard deviation of all amounts reimbursed is $3.00

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#### Solution Preview

n = 75

<X> = 93.70

sd = 34.55

number of incorrect reimbursements = 12

a.)

a = 0.05

Null hypothesis Ho: p - z*sd/sqrt(n) > po = 10% = 0.1

sample proportion p = 12/75 = 4/15 = 0.16

sd = ...

#### Solution Summary

The following involves medicare payments and determining the % of reimbursements where an incorrect amount was provided. The following hypothesis is tested: Is the proportion of incorrect reimbursements in a population less than 10%? The hypothesis test is conducted, p-value is reported, and a test of sample size is reported.