Question

Many consumer groups feel that the U.S. Food and Drug Administration (FDA) drug approval process is too easy and, as a result, too many drugs are approved that are later found to be unsafe. On the other hand, a number of industry lobbyists have pushed for a more lenient approval process so that pharmaceutical companies can get new drugs approved more easily and quickly. The FDA wants to set up a hypothesis test to show that the new drug is safe before approving it by assuming it to be unsafe.
If you reject the null hypothesis based on the evidence, your conclusion should be that:

a. there is insufficient evidence that the new drug is safe
b. there is insufficient evidence that the new drug is unsafe
c. there is sufficient evidence that the new drug is safe
d. there is sufficient evidence that the new drug is unsafe

If you do not reject the null hypothesis based on the evidence, your conclusion should be that:

a. there is insufficient evidence that the new drug is safe
b. there is insufficient evidence that the new drug is unsafe
c. there is sufficient evidence that the new drug is safe
d. there is sufficient evidence that the new drug is unsafe

Answer 1

Answer:

If we reject the null hypothesis based on the evidence, then our  conclusion should be Option c.

If we do not reject the null hypothesis based on the evidence, then our  conclusion should be Option a.

Step-by-step explanation:

We are given that the FDA wants to set up a hypothesis test to show that the new drug is safe before approving it by assuming it to be unsafe.

So, Null hypothesis, $H_0$ = New drug is unsafe

 Alternate Hypothesis, $H_1$ = New drug is safe

Now, if we reject the null hypothesis based on the evidence, then our  conclusion should be that :

There is sufficient evidence to believe that the new drug is safe because rejecting null hypothesis means that alternate hypothesis is accepted with required evidence.

And If we do not reject the null hypothesis based on the evidence, then our  conclusion should be that :

There is insufficient evidence to believe that the new drug is safe because not rejecting null hypothesis means that we are not ready with enough evidence to assume that new drug is safe.