Question

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.)

Answer 1

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