A company is testing a new affordable drug that may have theability to strengthe

Question

A company is testing a new affordable drug that may have theability to strengthen a patient's immune system that is weak by thespecific virus. Thirty monkeys infected with the virus havebeen given the drug. Researchers intend to wait 6 weeks andthen count the number of monkeys whose immunological response showa marked improvement. Any inexpensive drug capable of beingeffective 60% of the time would be considered as a majorbreakthough; medication whose chances of success are less than orequal to 50% are unlikely to have any commercial potential. The company hopes to avoid making either of two errors 1. rejectinga drug that would prove to be marketable, 2. spend money on a drugwhose effectiveness in the long run would be less than50%.

As a "decision rule" the manager decided that unless 16 or moremonkeys show improvement research on the drug should bediscontinued

a. what are the chances that the "16 or more" rule will cause thecompany to reject the drug even if it is 60% effective?

b. how often will teh "16 or more" rule allow a 50% effective drugto be perceived as a major breakthrough?

Explanation / Answer

Find P(rejecting the drug).
Let p = P(monkey willimprove)
Suppose p = 0.6.
Let X = # of monkeys that showed improvement.
X ~ Binomial(n = 30, p = 0.6)
P(rejecting the drug) = P(X < 16).
E(X) = np = 30 * 0.6 = 18
SE(X) = [ n * p * (1 – p) ] = [ 30 * 0.6 * 0.4] = 7.2 = 2.6833
Z = [ x - E(X) ] / SE(X) = (15.5 - 18) / 2.6833 = -0.9312
The 16 - 0.5 = 15.5 is to adjust for the continuity correction.
P(X < 16) = P(Z < -0.9312) = 0.1757

Find P(do not reject the drug).
Let p = P(monkey willimprove)
Suppose p = 0.5.
Let X = # of monkeys that showed improvement.
X ~ Binomial(n = 30, p = 0.5)
P(do not reject the drug) = P(X 16).
E(X) = np = 30 * 0.5 = 15
SE(X) = [ n * p * (1 – p) ] = [ 30 * 0.5 * 0.5] = 7.5 = 2.739
Z = [ x - E(X) ] / SE(X) = (15.5 - 15) / 2.739 = 0.1826
The 16 - 0.5 = 15.5 is to adjust for the continuity correction.
P(X 16) = P(Z > 0.1826) = 0.4256

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.