Question

Rhino viruses typically cause common colds. In a test of the effectiveness of echinacea, 35 of the 42 subjects treated with echinacea developed rhinovirus infections. In a placebo group, 80 of the 93 subjects developed rhinovirus infections. Use a 0.05 significance level to test the claim that echinacea has an effect on rhinovirus infections. What are the null and alternative hypotheses for the hypothesis​test? identify the test statistic and p-value

Answer 1

The null and alternative hypothesis

H0 : p1 =p2

Ha; p1 < p2

where p1 and p2 are population proportion subjects developed rhinovirus infections who are treated with echinacea and placebo respectively .

Note : As the claim is that  echinacea has an effect on rhinovirus infection , the alternative hypothesis is stated as p1<p2 , thus the test is left tailed .

Test statistic is

where

35 /42 = 0.8333

80/93 = 0.8602

P = (35+80) / (42+93) = 0.8519

Q=1-P= 0.1481

Thus

= -0.41

P value = P( z < -0.41 ) ( as this is a left tailed test )

From z table P( z < -0.41)= 0.3409

Since P value >0.05

We fail to reject H0

At 5% level there is not enough evidence to verify the claim that echinacea has an effect on rhinovirus infection.