Question

Pharmaceutical companies must subject each new drug to lengthy and involved testing before receiving the necessary permission from the Food and Drug Administration (FDA) to market the drug. The FDA's policy is that the pharmaceutical company must provide substantial evidence that a new drug is safe prior to receiving FDA approval, so that the FDA can confidently certify the safety of the drug to potential customers

(a) If the new drug were to be placed in a test of hypothesis framework, would the null hypothesis be that the drug is safe or unsafe? The alternative hypothesis?
(b) Desccribe the Type I and II errors in terms of this application.
(c) If the FDA wants to be very confident that the drug is safe before permitting it to be marketed, is it more important that α or β be small? Explain.

Answer 1

a) safe, alternative hypothesis is that drug is unsafe

b) Type I: Drug is unsafe

Type II: Drug is safe

c) yes

Explanation:

a) Null Hypothesis: Hypothesis stating that the claim is true and any difference in the result is only due to experimental error.

Alternate hypothesis: rejecting the claim.

b) type I error is incorrectly rejecting null hypothesis when it is actually true

type ii error is failure to reject null hypothesis when it is actually false

c) β is probability of type ii error

α is probabiltiy of type i error.

Both of these must be small for hypothesis testing

Answer 2

Answer and Explanation:

(a) Null hypothesis H0 : the new drug is safe.

Alternative hypothesis H1 : the drug is not safe.

(b) Type I error: Rejecting H0 when it is true. So, the drug is not taken when the drug is safe.

Type II error: Accepting H0 when it is not true. So, the drug is taken when the drug is not safe.

(c) Type II error is more harmful than type I error. So, the probability P(TypeII error) = \beta should be minimized to increase the power of the test 1-\beta.