Originating drug companies invent medications and give each drug 2 names, the brand name and the generic name. The brand name is simply what the manufacturer calls the product and the generic name represents the chemical compound of the drug. It takes many years, at least 20, before a drug can be manufactured as a generic; this is due to the patents that are put on the new medications.
While researching it is found that he volume of generic prescriptions, both new and refilled, as found to be over 41% in 1999. A sample has been conducted by running a report of all medications filled in one day, comprised of new and refilled prescriptions, at Foodtown Pharmacy in Lambertville, Michigan. The sample was taken from 301 prescriptions filled, of which 101 were filled with generic medication; the sample was conducted on January 27, 2003. With this information we can conclude whether or not 41% or more of prescriptions in the sample area are filled with generic medications in 2003.
Variables
n = 307 = = 0.329
a = 0.05 po = 0.41
Step 1: Null and Alternative Hypothesis
The null hypothesis is the tested sample proportion being equal or less than 41%. The alternative hypothesis is our sample proportion being greater than 41%. A one-tail test must be used in order to conclude whether or not more than 40% of prescriptions are filled with generic medication.
Ho : p ≤ 0.41
Ha : p > 0.41
Step 2: Test Statistic
The population proportion test statistic must be used due to the statistic that has been selected to test, because it is a percentage. We therefore use the following equation to compute the Z-value:
=
The following is a bell curve that describes the data that has just been calculated:
a = 0.05
0.4981
0 1.645 2.866
Step 3: Decision Rule
We are testing at a significance level of 0.05, which means that we reject the null hypothesis if the computed value of Z* is greater than 1.645. Because –2.886 is less than 1.645, we fail to reject the null hypothesis.
Reject Ho if Z > Z.05 = 1.645
–2.886 < 1.645, we fail to reject Ho.
Step 4: Significance Level
The p-value is calculated by subtracting the Z*-value area from alpha (selected level of significance), which is 0.05. The area at Z*=2.886 is 0.4981. The p-value is 0.0.5 – 0.4981, which is 0.0019. The General Rule of Thumb allows us to reject the null hypothesis because the p-value is less than 0.01. This means that there is less than a 1% chance that our null hypothesis could be rejected. This helps to support that the probability of rejecting the null hypothesis holds truth.
Step 5: Compute and Decision Made
Based on the tests statistic and the p-value , the sample that was selected does not support the statistic being tested. This means that 41% or more of prescriptions in are not filled with generic medications, in the area that the sample population was taken from. Therefore we can state: In the area of northern Toledo, OH and southern Monroe, MI less than 41% of prescriptions are filled with generic medications.
Conclusion
Since the statistic selected was not supported by the sample populatinon, what could the reasoning be that less than 41% of prescriptions are filled with generic drugs? It is possible that Doctors in this area are requesting brand names by writing DAW (dispense as written) prescriptions, which mean to only dispense the brand name, Another suggestion is that the statistic that was being tested is from 1999, and the sample used was taken in 2003. Many new drugs have since been introduced to the market and the doctors are prescribing the new medications. And, since a patent on a drug can last 20 years or more, the new drug selection for doctors prescriptions has increased much more than the generic drug selection. Whatever the reasoning may be, it can be said that less than 41% of all prescriptions filled in the area tested are filled with generic drugs.
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http://www.tevapharmusa.com/factsabout.html
http://www.umich.edu/~benefits/new/series/091800.htm
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