Question

After a name-brand drug has been sold for several years, the Food and Drug Administration (FDA) will allow other companies to produce a generic equivalent. The FDA will permit the generic drug to be sold as long as there isn't convincing evidence that it is less effective than the name-brand drug. For a proposed generic drug intended to lower blood pressure, the following hypotheses will be us

where

$\mu \mathrm{G}=$true mean reduction in blood pressureusing the generic drug $\mu \mathrm{G}=$true mean reduction in blood pressureusing the name@brand drug

${\mu }_G=$true mean reduction in blood pressure

using the generic drug

${\mu }_G=$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 convincing evidence that the generic drug is less effective, when in reality it is less effective.

b. The FDA finds convincing evidence that the generic drug is less effective, when in reality it is equally effective.

c. The FDA finds convincing evidence that the generic drug is equally effective, when in reality it is less effective.

d. The FDA fails to find convincing evidence that the generic drug is less effective, when in reality it is less effective.

e. The FDA fails to find convincing evidence that the generic drug is less effective, when in reality it is equally effective.

Short answer

Type I error is option

b. The FDA finds convincing evidence that the generic drug is less effective, when in reality it is equally effective.

Step-by-step solution

Given information

Given in the question that, after a name-brand drug has been sold for several years, the Food and Drug Administration (FDA) will allow other companies to produce a generic equivalent. The FDA will permit the generic drug to be sold as long as there isn't convincing evidence that it is less effective than the name-brand drug. For a proposed generic drug intended to lower blood pressure, the following hypotheses will be used:

$\mathrm{H}0:\mu \mathrm{G}=\mu \mathrm{N}\text{versus}\mathrm{Ha}:\mu \mathrm{G}<\mu \mathrm{N}{H}_0:{\mu }_G={\mu }_N\text{versus}{H}_a:{\mu }_G\&\text{lt};{\mu }_N$

where

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

$\mu \mathrm{G}=$true mean reduction in blood pressure using the name@brand drug

In the context of this situation, We need to find a Type I error from the options.

Explanation

Given,

$H_0:{\mu }_G={\mu }_N$

$H_1:{\mu }_G\ne {\mu }_N$

A Type l error occurs when the null hypothesis is rejected when it is true.

When the two means are actually exercised, the right statement should be that there is no convincing evidence that the mean ${\mu }_G$is less than the mean ${\mu }_N$. The accurate statement appears to be (b), i.e., the FDA discovers persuasive evidence that the generic drug is less effective than the brand-name drug, when it is actually equally effective. As a result, option (b) is the proper choice.