Question

In a clinical​ trial, 22 out of 826 patients taking a prescription drug daily complained of flulike symptoms. Suppose that it is known that 2.1​% of patients taking competing drugs complain of flulike symptoms. Is there sufficient evidence to conclude that more than 2.1​% of this​ drug's users experience flulike symptoms as a side effect at the alpha equals 0.01 level of​ significance? Because np 0 left parenthesis 1 minus p 0 right parenthesisequals nothing ▼ not equals greater than equals less than ​10, the sample size is ▼ greater than less than ​5% of the population​ size, and the sample ▼ is given to not be random, can be reasonably assumed to be random, cannot be reasonably assumed to be random, is given to be random, the requirements for testing the hypothesis ▼ are are not satisfied. ​(Round to one decimal place as​ needed.)

Answer 1

Solution:

Given:

n = 826

x = Number of  patients taking a prescription drug daily complained of flulike symptoms.

x = 22

We have to test if there is sufficient evidence to conclude that more than 2.1​% of this​ drug's users experience flulike symptoms as a side effect at the alpha equals 0.01 level of​ significance

Because np₀ (1 - p₀ ) = 826*0.021*(1-0.021) =  17.0  greater than 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.

Step 1) State H0 and H1:

H0: p = 0.021 Vs H1: p > 0.021

Step 2) test statistic:

where

thus

Step 3) Find p-value

p-value = P( Z> z )

p-value = P( Z>1.13)

p-value =1 - P( Z<1.13)

Look in z table for z = 1.1 and 0.03 and find corresponding area.

P( Z < 1.13) = 0.8708

p-value =1 - P( Z<1.13)

p-value =1 - 0.8708

p-value = 0.1292

Step 4) Decision Rule:
Reject null hypothesis H0, if P-value < 0.01 level of significance, otherwise we fail to reject H0

Since p-value = 0.1292 > 0.01 level of significance, we fail to reject H0.

Step 5) Conclusion:

At 0.01 level of​ significance,  there is not sufficient evidence to conclude that more than 2.1​% of this​ drug's users experience flulike symptoms as a side effect.