Question

Suppose a name-brand drug has been deemed effective for reducing hypertension (high blood pressure). The developing company gets to keep a patent on the drug for a specific period of time before other companies can develop a generic form of the drug. Suppose the patent period is about to expire, and another company produces a generic version of this drug. The Food and Drug Administration (FDA) wants to know whether the generic drug is at least as effective as the name-brand drug in reducing blood pressure.

The following hypotheses will be used:

$H_0:{\mu }_g={\mu }_n$vs $H_a:{\mu }_g<{\mu }_n$

where

${\mu }_g=$true mean reduction in blood pressure using the generic drug

${\mu }_n=$true mean reduction in blood pressure using the name-brand drug. In the context of this situation, which of the following describes a Type I error?

(a) The FDA finds sufficient evidence that the generic drug does not reduce blood pressure as much as the namebrand drug when, in fact, it does not.

(b) The FDA finds sufficient evidence that the generic drug does not reduce blood pressure as much as the namebrand drug when, in fact, it does.

(c) The FDA finds sufficient evidence that the generic drug does reduce blood pressure as much as the namebrand drug when, in fact, it does not.

(d) The FDA finds sufficient evidence that the generic drug does reduce blood pressure as much as the namebrand drug when, in fact, it does.

(e) The FDA does not find sufficient evidence that the generic drug is as effective in reducing blood pressure as the name-brand drug when, in fact, it is.

Short answer

(c) The FDA finds sufficient evidence that the generic drug does reduce blood pressure as much as the name-brand drug when,in fact , it does not.

Step-by-step solution

Given information

We are given that a name-brand drug has been deemed effective for reducing hypertension. The Food and Drug Administration (FDA) wants to know whether the generic drug is at least as effective as the name-brand drug in reducing blood pressure. The hypothesis used is : $H_0:{\mu }_g={\mu }_n$ vs $H_a:{\mu }_g<{\mu }_n$

Simplify

As we know, when we did not accept the null hypothesis,we are already concluding that name-brand drug has low of a reduction than generic drug.

Where as Type I rejects the null drug hypothesis stating it as not true, when in fact it is true.

Therefore, the FDA finds sufficient evidence that the generic drug does reduce blood pressure as much as the name-brand drug when,in fact , it does not.