Question

Rhino viruses typically cause common colds. In a test of the effectiveness of​ echinacea,

4040

of the

4545

subjects treated with echinacea developed rhinovirus infections. In a placebo​ group,

7777

of the

9292

subjects developed rhinovirus infections. Use a

0.010.01

significance level to test the claim that echinacea has an effect on rhinovirus infections. Complete parts​ (a) through​ (c) below.

a. Test the claim using a hypothesis test.

Consider the first sample to be the sample of subjects treated with echinacea and the second sample to be the sample of subjects treated with a placebo. What are the null and alternative hypotheses for the hypothesis​ test?

What is the test statistic?

The P-value?

Answer 1

Test statistic :

Test statistic = 0.81

P value :

with z= 0.81 ( two tailed )  

we get p value = 0.4179

Using the P-value approach: The p-value is p = 0.4179, and since p=0.4179 ≥ 0.01, it is concluded that the null hypothesis is not rejected.

Conclusion

It is concluded that the null hypothesis Ho is not rejected. Therefore, there is not enough evidence to claim that

echinacea has an effect on rhinovirus infections. at the 0.01 significance level.