MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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Rhino viruses typically cause common colds. In a test of the effectiveness of​ echinacea, 33 of the 38 subjects treated with echinacea developed rhinovirus infections. In a placebo​ group, 101 of the 114 subjects developed rhinovirus infections. Use a0.05 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?
A.
H0​:
p1=p2
H1​:
p1>p2
 
B.
H0​:
p1≤p2
H1​:
p1≠p2
 
C.
H0​:
p1=p2
H1​:
p1<p2
 
D.
H0​:
p1=p2
H1​:
p1≠p2
Your answer is correct.
 
E.
H0​:
p1≥p2
H1​:
p1≠p2
 
F.
H0​:
p1≠p2
H1​:
p1=p2
 
 
Identify the test statistic.
 
Identify the​ P-value.
 
What is the conclusion based on the hypothesis​ test?
The​ P-value is____ the significance level of α=0.05​, so the null hypothesis. There sufficient evidence to support the claim that echinacea treatment has an effect.
 
b. Test the claim by constructing an appropriate confidence interval.
 
The 95​% confidence interval is___< (p1−p2)<___.
(Round to three decimal places as​ needed.)
 
What is the conclusion based on the confidence​ interval?
 
Because the confidence interval limits____ 0, there ___ appear to be a significant difference between the two proportions. There____
evidence to support the claim that echinacea treatment has an effect.
c. Based on the​ results, does echinacea appear to have any effect on the infection​ rate?
 
A.Echinacea does not appear to have a significant effect on the infection rate.
B.Echinacea does appear to have a significant effect on the infection rate. There is evidence that it lowers the infection rate.
C.Echinacea does appear to have a significant effect on the infection rate. There is evidence that it increases the infection rate.
D.The results are inconclusive.
 
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