2. Pharmaceutical companies spend billions of dollars per year on research and development of new drugs. The pharmaceutical company 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 phar- maceutical 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 consumers. (a) If the new drug testing 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? (In an actual test, "safety" could be quantified using population parameters; Problem 7 is a conceptual exercise.) Fill in the blanks below. The null hypothesis would be that the drug is be that the drug is and the alternative hypothesis would (b) Given the choice of null and alternative hypotheses in part (a), describe the Type I and Type II errors in terms of this application. Define a and 3 in terms of this application. Fill in the blanks below. The Type I error for this problem would be to conclude that the drug is when the drug

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2. Pharmaceutical companies spend billions of dollars per year on research and development of new drugs. The
pharmaceutical company 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 phar-
maceutical 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 consumers.
(a) If the new drug testing 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? (In an actual test, "safety" could be quantified using
population parameters; Problem 7 is a conceptual exercise.) Fill in the blanks below.
The null hypothesis would be that the drug is
be that the drug is
and the alternative hypothesis would
(b) Given the choice of null and alternative hypotheses in part (a), describe the Type I and Type II errors in terms
of this application. Define a and 3 in terms of this application. Fill in the blanks below.
The Type I error for this problem would be to conclude that the drug is --
is actually
--- when the drug
The Type II error for this problem would be to conclude that the drug is
when the drug is actually
In this application a is the probability of concluding that a drug
safe when actually
it
and 3 is the probability of concluding that a drug
safe.
safe
when the drug actually
(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 a or be small? Circle the correct answer.
(i) The value of a should be minimized to minimize the risk of falsely concluding the drug is safe when it is not
safe and could hurt people.
(ii) The value of B should be minimized to minimize the risk of falsely concluding the drug is not safe when it
is safe and could help people.
(iii) The value of a should be minimized to minimize the risk of falsely concluding the drug is not safe when it
is safe and could help people.
(iv) The value of 3 should be minimized to minimize the risk of falsely concluding the drug is safe when it is not
safe and could hurt people.
2
Transcribed Image Text:2. Pharmaceutical companies spend billions of dollars per year on research and development of new drugs. The pharmaceutical company 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 phar- maceutical 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 consumers. (a) If the new drug testing 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? (In an actual test, "safety" could be quantified using population parameters; Problem 7 is a conceptual exercise.) Fill in the blanks below. The null hypothesis would be that the drug is be that the drug is and the alternative hypothesis would (b) Given the choice of null and alternative hypotheses in part (a), describe the Type I and Type II errors in terms of this application. Define a and 3 in terms of this application. Fill in the blanks below. The Type I error for this problem would be to conclude that the drug is -- is actually --- when the drug The Type II error for this problem would be to conclude that the drug is when the drug is actually In this application a is the probability of concluding that a drug safe when actually it and 3 is the probability of concluding that a drug safe. safe when the drug actually (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 a or be small? Circle the correct answer. (i) The value of a should be minimized to minimize the risk of falsely concluding the drug is safe when it is not safe and could hurt people. (ii) The value of B should be minimized to minimize the risk of falsely concluding the drug is not safe when it is safe and could help people. (iii) The value of a should be minimized to minimize the risk of falsely concluding the drug is not safe when it is safe and could help people. (iv) The value of 3 should be minimized to minimize the risk of falsely concluding the drug is safe when it is not safe and could hurt people. 2
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