Z = (Round to two decimal places as needed.) P-value= The P-value is (Less than/ greater than) the significance level of α=0.05, so (Fail to reject / reject) the null hypothesis. There (There is/ is not) sufficient evidence to support the claim that echinacea treatment has an effect
Rhino viruses typically cause common colds. In a test of the effectiveness of echinacea,
40
of the
46
subjects treated with echinacea developed rhinovirus infections. In a placebo group,
87
of the
104
subjects developed rhinovirus infections. Use a
0.01
significance level to test the claim that echinacea has an effect on rhinovirus infections. Complete parts (a) through (c) below.
- 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
E.
H0:
p1=p2
H1:
p1>p2
F.
H0:
p1≤p2
H1:
p1≠
Identify the test statistic.
Z =
(Round to two decimal places as needed.)
P-value=
The P-value is (Less than/ greater than) the significance level of α=0.05, so (Fail to reject / reject) the null hypothesis. There (There is/ is not) sufficient evidence to support the claim that echinacea treatment has an effect
- 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 (Include/ Do not include) 0, there (Does / Doe not) appear to be a significant difference between the two proportions. There (Is not / Is) evidence to support the claim that echinacea treatment has an effect.
- 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 increases 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 not appear to have a significant effect on the infection rate.
D.
The results are inconclusive
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