Question

# In a clinical​ trial, 17 out of 863 patients taking a prescription drug daily complained of...

In a clinical​ trial, 17 out of 863 patients taking a prescription drug daily complained of flulike symptoms. Suppose that it is known that 1.6​% of patients taking competing drugs complain of flulike symptoms. Is there sufficient evidence to conclude that more than 1.6​% of this​ drug's users experience flulike symptoms as a side effect at the α=0.1 level of​ significance?

Because np (01−p0) =__?__

>

=

<

​10, the sample size is

less than

greater than

​5% of the population​ size, and the sample

is given to not be random,

is given to be random,

cannot be reasonably assumed to be random,

can be reasonably assumed to be random,

the requirements for testing the hypothesis

are

are not

satisfied.

​(Round to one decimal place as​ needed.)

p0 = 1.6% = 0.016

np0 (1-p0) = 863 * 0.016 * (1- 0.016) = 13.587

Because, np0 (1-p0) > 10

the sample size is less than ​5% of the population​ size, and the sample

can be reasonably assumed to be random

the requirements for testing the hypothesis

are satisfied.

H0: p0 = 0.016

H1: p0 > 0.016

Standard error of proportion = = 0.00427

Sample proportion, p = 17/863 = 0.0197

Test statistic, z = (p - p0) / Std error

= (0.0197 - 0.016) / 0.00427

= 0.8665

P-value = P(z > 0.8665) = 0.1931

Since, p-value is greater than 0.01 significance level, we fail to reject null hypothesis H0 and there is no sufficient evidence to conclude that more than 1.6​% of this​ drug's users experience flulike symptoms as a side effect