MATLAB: An Introduction with Applications
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ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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Transcribed Image Text:Rhino viruses typically cause common colds. In a test of the effectiveness of echinacea, 33 of the 39 subjects treated with echinacea developed
rhinovirus infections. In a placebo group, 99 of the 113 subjects developed rhinovirus infections. Use a 0.05 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?
O A. Ho: P1 2 P2
H1: P1 # P2
B. Ho: P1 + P2
O C. Ho: P1 = P2
H1: P1 = P2
H: P1 # P2
F. Ho: P1 = P2
E. Ho: P1 sP2
H4: P1 # P2
D. Ho: P1 = P2
H1: P1 > P2
H4: P1 <P2
Identify the test statistic.
Z=
(Round to two decimal places as needed.)
Identify the P-value.
P-value =
(Round to three decimal places as needed.)
What is the conclusion based on the hypothesis test?
The P-value is
the significance level of a = 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 isO< (P1 - P2) <U.
(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.
Transcribed Image Text:c. Based on the results, does echinacea appear to have any effect on the infection rate?
A. Echinacea does appear to have a significant effect on the infection rate. There is evidence that it lowers the infection rate.
B. Echinacea does appear to have a significant effect on the infection rate. There is evidence that it increases the infection rate.
C. Echinacea does not appear to have a significant effect on the infection rate.
O D. The results are inconclusive.
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