Rhino viruses typically cause common colds In a test of the

Rhino viruses typically cause common colds. In a test of the effectiveness of echinacea, 39 of the 45 subjects treated with echinacea developed rhinovirus infections. In a placebo group, 87 of the 101 subjects developed rhinovirus infections. Use a 0.01significance 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?

A. H0: p1 = p 2

H1: p 1 p2

B.

H0: p1 p 2

H1: p 1 = p2

C.

H0: p1 greater then or equal to p 2

H1: p 1 p2

D.

H0: p1 = p2

H1: p1 < p 2

E. H0: p 1 p 2

H1: p 1 p 2

F. H0: p1 = p 2

H1: p1 > p2

2. Identify the test statistic.

z= ???

(Round to two decimal places as needed.)

3. Identify the P-value.

P-value= ???

(Round to three decimal places as needed.)

Solution

Null, Ho: p1 = p2
Alternate, H1: p1 != p2
Test Statistic
Sample 1 : X1 =39, n1 =45, P1= X1/n1=0.867
Sample 2 : X2 =87, n2 =101, P2= X2/n2=0.861
Finding a P^ value For Proportion P^=(X1 + X2 ) / (n1+n2)
P^=0.863
Q^ Value For Proportion= 1-P^=0.137
we use Test Statistic (Z) = (P1-P2)/(P^Q^(1/n1+1/n2))
Zo =(0.867-0.861)/Sqrt((0.863*0.137(1/45+1/101))
Zo =0.086
| Zo | =0.086
Critical Value
The Value of |Z | at LOS 0.01% is 2.576
We got |Zo| =0.086 & | Z | =2.576
Make Decision
Hence Value of |Zo | < | Z | and Here we Do not Reject Ho
P-Value: Two Tailed ( double the one tail ) -Ha : ( P != 0.0857 ) = 0.9317
Hence Value of P0.01 < 0.9317,Here We Do not Reject Ho

[ANSWERS]
1. H0: p1 = p 2
H1: p 1 p2

2. Zo =0.09

3. Two Tailed ( double the one tail ) -Ha : ( P != 0.0857 ) = 0.9317