Question

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

44 of the 51 subjects treated with echinacea developed rhinovirus infections. In a placebo​ group,

95 of the 112 subjects developed rhinovirus infections. Use a 0.01 significance level to test the claim that echinacea has an effect on rhinovirus infections.

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?

Answer 1

#Solution:

Null hypothesis and Alternate hypothesis are

Ho : p1 = p2

Ha : p1 p2

1 =x1/n1= 44/51=0.8627

2 =x2/n2= 95/112=0.8482

Standard error = √{p*(1-p)}*√{(1/n1)+(1/n2)}

=√(0.8527*(1-.8527)*((1/51)+(1/112))

=0.0598

Test statistics z = (1-2)/standard error

After substitution

Test statistics z = 0.24

From z table, P(Z>0.24) = 0.4041

As the test is two tailed

So, P-Value = 2*0.4041 = 0.8081

As the obtained P-Value is greater than the given significance 0.01

We fail to reject the null hypothesis Ho

We do not have enough evidence to conclude that echinacea has an effect on rhino virus infections.