Question

In a clinical​ trial, 25 out of 822 patients taking a prescription drug daily complained of flulike symptoms. Suppose that it is known that 2.7​% of patients taking competing drugs complain of flulike symptoms. Is there sufficient evidence to conclude that more than 2.7% of this​ drug's users experience flulike symptoms as a side effect at the α=0.1 level of​ significance?
Because np 0 ( 1- p 0) = ?
▼
<
>
=
≠
​10, the sample size is
▼
greater thangreater than
less thanless than
​5% of the population​ size, and the sample
▼
is given to be random,
cannot be reasonably assumed to be random,
can be reasonably assumed to be random,
is given to not be random,
the requirements for testing the hypothesis
▼
are
are not
satisfied.

Answer 1

Given that, n = 822 and x = 25

p₀ = 0.027

np₀(1-p₀) = 822 * 0.027 * ( 1 - 0.027) = 21.5948

Because, np₀(1-p₀) = 21.6 greater than ( > )10, the sample size greater than 5% of the population size and the sample can be reasonably assumed to be random the requirements for testing the hypothesis are satisfied.

The null and the alternative hypotheses are,

H₀ : p = 0.027 versus H₁ : p > 0.027

Using TI-84 calculator we get,

Test statiatic is, Z₀ = 0.60

p-value = 0.2730

Since, the p-value = 0.2730 > , do not reject the null hypothesis and conclude that there is not sufficient evidence that more than 2.7% of the users experience flulike symptoms.