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Eduardwww [97]
3 years ago
15

One hundred sixty people who suffer from painful diabetic neuropathy have volunteered to participate in a study. Eighty are sele

cted at random and are given the drug gabapentin, which, although originally intended to prevent epileptic seizures, has properties that may make it useful to alleviate neuropathy. The remaining participants are given a placebo. A neurologist evaluates the symptoms of all volunteers after two months to determine if there has been substantial improvement in the severity of the symptoms.
Does the use of volunteers make this study invalid?

a. yes, because of volunteer bias no, because blocking was used.
b. yes, because there is no way to determine the effect of gabapentin on people that do not have symptoms of neuropathy.
c. no, because the subjects are randomly assigned to treatment groups.
Mathematics
1 answer:
Varvara68 [4.7K]3 years ago
8 0

Answer:

C. No, because the subjects are randomly assigned to treatment groups

Step-by-step explanation:

We are told that 80 people are selected at random and are given the drug gabapentin.

Also that the remaining people are given the placebo.

This means that they are randomly assigned treatment groups and so it is a completely randomized block design and as such the use of volunteers doesn't make it invalid.

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a) 0.21% probability that there are no bad peaches in the peach cobbler.

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Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

The order in which the peaches are chosen is not important. So the combinations formula is used to solve this question.

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C_{n,x} = \frac{n!}{x!(n-x)!}

(a) If you make a peach cobbler of 12 peaches randomly selected from the box, what is the probability that there are no bad peaches in the peach cobbler?

Desired outcomes:

12 good peaches, from a set of 12. So

D = C_{12,12} = \frac{12!}{12!(12 - 12)!} = 1

Total outcomes:

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0.21% probability that there are no bad peaches in the peach cobbler.

(b) What is the probability of having at least 1 bad peach in the peach cobbler?

Either there are no bad peaches, or these is at least 1. The sum of the probabilities of these events is 100%. So

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(c) What is the probability of having exactly 2 bad peaches in the peach cob- bler?

Desired outcomes:

2 bad peaches, from a set of 3.

One good peach, from a set of 12.

D = C_{3,2}*C_{12,1} = \frac{3!}{2!(3-2)!}*\frac{12!}{1!(12 - 1)!} = 36

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12 peaches, from a set of 15. So

T = C_{15,12} = \frac{15!}{12!(15 - 12)!} = 455

Probability:

p = \frac{D}{T} = \frac{36}{455} = 0.0791

7.91% probability of having exactly 2 bad peaches in the peach cobbler.

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