In: Statistics and Probability
Rhino viruses typically cause common colds. In a test of the effectiveness of echinacea, 42 of the 49 subjects treated with echinacea developed rhinovirus infections. In a placebo group, 88
of the 105. 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.
Test the claim using a hypothesis test.
Upper H 0H0:
Identify the test statistic.
zequals=nothing
(Round to two decimal places as needed.)
Identify the P-value.
P-valueequals=nothing
(Round to three decimal places as needed.)
What is the conclusion based on the hypothesis test?
The P-value is
▼
greater than
less than
the significance level of
alphaαequals=0.050.05,
so
▼
reject
fail to reject
the null hypothesis. There
▼
is
is not
sufficient evidence to support the claim that echinacea treatment has an effect.
b. Test the claim by constructing an appropriate confidence interval.
The
9595%
confidence interval is
nothingless than<left parenthesis p 1 minus p 2 right parenthesisp1−p2less than<nothing.
(Round to three decimal places as needed.)
What is the conclusion based on the confidence interval?
Because the confidence interval limits
▼
do not include
include
0, there
▼
does
does not
appear to be a significant difference between the two proportions. There
▼
is
is not
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 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.
p 1p1less than or equals≤p 2p2
Upper H 1H1:
p 1p1not equals≠p 2p2
B.
Upper H 0H0:
p 1p1equals=p 2p2
Upper H 1H1:
p 1p1greater than>p 2p2
C.
Upper H 0H0:
p 1p1equals=p 2p2
Upper H 1H1:
p 1p1less than<p 2p2
D.
Upper H 0H0:
p 1p1greater than or equals≥p 2p2
Upper H 1H1:
p 1p1not equals≠p 2p2
E.
Upper H 0H0:
p 1p1equals=p 2p2
Upper H 1H1:
p 1p1not equals≠p 2p2
F.
Upper H 0H0:
p 1p1not equals≠p 2p2
Upper H 1H1:
p 1p1equals=p 2