In a study of treatments for very painful "cluster" headaches, 158 patients were treated with oxygen and 150 other patients were given a placebo consisting of ordinary air. Among the 158 patients in the oxygen treatment group, 126 were free from headaches 15 minutes after treatment. Among the 150 patients given the placebo, 30 were free from headaches 15 minutes after treatment. Use a 0.01 significance level to test the claim that the oxygen treatment is effective. Complete parts (a) through (c) below. Test the claim using a hypothesis test. Consider the first sample to be the sample of patients treated with oxygen and the second sample to be the sample of patients given 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: p1p2 F. H0: p1=p2 H1: p1≠p2 Identify the test statistic. z=nothing (Round to two decimal places as needed.) Identify the P-value. P-value=nothing (Round to three decimal places as needed.) What is the conclusion based on the hypothesis test? The P-value is ▼ less than greater than the significance level of α=0.01, so ▼ reject fail to reject the null hypothesis. There ▼ is not sufficient is sufficient evidence to support the claim that the cure rate with oxygen treatment is higher than the cure rate for those given a placebo. Test the claim by constructing an appropriate confidence interval. The 98% confidence interval is nothing
In a study of treatments for very painful "cluster" headaches,
158
patients were treated with oxygen and
150
other patients were given a placebo consisting of ordinary air. Among the
158
patients in the oxygen treatment group,
126
were free from headaches 15 minutes after treatment. Among the
150
patients given the placebo,
30
were free from headaches 15 minutes after treatment. Use a
0.01
significance level to test the claim that the oxygen treatment is effective. Complete parts (a) through (c) below.
- Test the claim using a hypothesis test.
Consider the first sample to be the sample of patients treated with oxygen and the second sample to be the sample of patients given 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≠p2
Identify the test statistic.
z=nothing
(Round to two decimal places as needed.)
Identify the P-value.
P-value=nothing
(Round to three decimal places as needed.)
What is the conclusion based on the hypothesis test?
The P-value is
▼
less than
greater than
the significance level of
α=0.01,
so
▼
reject
fail to reject
the null hypothesis. There
▼
is not sufficient
is sufficient
evidence to support the claim that the cure rate with oxygen treatment is higher than the cure rate for those given a placebo.
- Test the claim by constructing an appropriate confidence interval.
The
98%
confidence interval is
nothing<p1−p2<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, it appears that the two cure rates are
▼
equal.
not equal.
Because the confidence interval limits include
▼
positive and negative
only negative
only positive
values, it appears that the cure rate is
▼
the same
higher
lower
for the oxygen treatment than for the placebo.
- Based on the results, is the oxygen treatment effective?
A.
The results suggest that the oxygen treatment is not effective in curing "cluster" headaches because the cure rates appear to be the same.
B.
The results suggest that the oxygen treatment is not effective in curing "cluster" headaches because the cure rate for the oxygen treatment appears to be lower than that of the placebo.
C.
The results suggest that the oxygen treatment is effective in curing "cluster" headaches.
D.
The results are inconclusive.
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