A company is testing a new affordable drug that may have theability to strengthe
ID: 2955056 • Letter: A
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).
X ~ Binomial(n = 30, p = 0.6)
x
P(X = x)
0
1.15292E-12
1
5.18815E-11
2
1.12842E-09
3
1.57979E-08
4
1.59954E-07
5
1.24764E-06
6
7.79775E-06
7
4.01027E-05
8
0.000172943
9
0.000634124
10
0.001997491
11
0.005447702
12
0.012938292
13
0.026871837
14
0.048945131
15
0.07831221
16
0.110126545
17
0.136038673
18
0.147375229
19
0.139618638
20
0.115185376
21
0.082275269
22
0.050487097
23
0.026341094
24
x
P(X = x)
0
1.15292E-12
1
5.18815E-11
2
1.12842E-09
3
1.57979E-08
4
1.59954E-07
5
1.24764E-06
6
7.79775E-06
7
4.01027E-05
8
0.000172943
9
0.000634124
10
0.001997491
11
0.005447702
12
0.012938292
13
0.026871837
14
0.048945131
15
0.07831221
16
0.110126545
17
0.136038673
18
0.147375229
19
0.139618638
20
0.115185376
21
0.082275269
22
0.050487097
23
0.026341094
24
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