United Medicine, Inc., claims that a drug, Viro, significantly relieves the symp

Question

United Medicine, Inc., claims that a drug, Viro, significantly relieves the symptoms of a certain viral infection for 80 percent of all patients. Suppose that this drug is given to 13 randomly selected patients who have been diagnosed with the viral infection.

Let x equal the number of the 13 randomly selected patients whose symptoms are significantly relieved. What distribution describes the random variable x ? (Round your answers to 1 decimal place.)

Assuming that the company's claim is correct, find P(x 5). (Round your answer to 4 decimal places.)

Suppose that of the 13 randomly selected patients, 5 have had their symptoms significantly relieved by Viro. Based on the probability in part b, would you believe the claim of United Medicine, Inc.?

United Medicine, Inc., claims that a drug, Viro, significantly relieves the symptoms of a certain viral infection for 80 percent of all patients. Suppose that this drug is given to 13 randomly selected patients who have been diagnosed with the viral infection.

Explanation / Answer

a) BInomial n = 13, p = 0.80

Bin prob P(X=r) = nCr p^r q^(n-r)

b) P(X<=5) =0.0012

c) 80% of 13 = 10.4

Actual proportion = 5/13 = 0.3846

H0: p = 0.80

Ha: p <0.80

p difference = 0.3846-0.80 =- 0.6154

Std error = rt pq = 0.4

Hence z = -0.6154/0.4

= -0.1539

p value = 0.4388

Since p > 0.10 accept null hypothesis.

Prob of 5 or fewer is >1%

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