SOLUTION: Late payment of medical claims can add to the cost of health care. The auditing firm of Dewey, Cheatham, and Howe has discovered that for one insurance company, 85.1% of the claim

Question 451410: Late payment of medical claims can add to the cost of health care. The auditing firm of Dewey, Cheatham, and Howe has discovered that for one insurance company, 85.1% of the claims were paid in full when first submitted based on a sample of 200 claims. Suppose that the insurance company developed a new payment system in an effort to increase this percentage. A sample of 200 claims processed under this new system revealed that 180 of the claims were paid in full when first submitted. At the 5% level of significance, is there evidence that the population proportion of claims paid in full under this new system is higher than the proportion of claims paid in full under the old system?
Q-2a: State the null hypothesis
Q-2b: State the alternative hypothesis.
Q-2c: Perform the hypothesis test and state your conclusions and evidence.

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Late payment of medical claims can add to the cost of health care. The auditing firm of Dewey, Cheatham, and Howe has discovered that for one insurance company, 85.1% of the claims were paid in full when first submitted based on a sample of 200 claims.
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Suppose that the insurance company developed a new payment system in an effort to increase this percentage. A sample of 200 claims processed under this new system revealed that 180 of the claims were paid in full when first submitted.
-----------------------------
At the 5% level of significance, is there evidence that the population proportion of claims paid in full under this new system is higher than the proportion of claims paid in full under the old system?
------

Q-2a: State the null hypothesis
Ho: p(new)-p(old) = 0
--------------------------------
Q-2b: State the alternative hypothesis.
Ha: p(new)-p(old) > 0 (claim)
--------------------------------
Q-2c: Perform the hypothesis test and state your conclusions and evidence.
---
I ran a 2PropZTest with on my TI-84 and got the following:
test statistic: z = 1.5119
p-value = 0.0653
---
Conclusion: Since the p-value is greater than 5%, fail to
reject Ho. The test results do not support the claim.
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Cheers,
Stan H.
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