Question

**Identify the null hypothesis, alternative hypothesis,
test statistic, P-value, conclusion about the null hypothesis, and
final conclusion that addresses the original claim. Use the P-value
method.**

In a study of treatments for very painful “cluster headaches”, 144 patients were treated with oxygen and 154 other patients were given a placebo consisting of ordinary air. Among the 144 patients in the oxygen treatment group, 116 were free from headaches 15 minutes after treatment. Among the 154 patients given the placebo, 33 were free from headaches 15 minutes after treatment.

(a) Construct a 98% confidence interval estimate of the difference between the cure rate of the oxygen treatment, p1 and the cure rate of the placebo, p2.

(b) What does the confidence interval suggest about the effectiveness of the oxygen treatment? Why?

Answer #1

a)

Here, , n1 = 144 , n2 = 154

p1cap = 0.8056 , p2cap = 0.2143

Standard Error, sigma(p1cap - p2cap),

SE = sqrt(p1cap * (1-p1cap)/n1 + p2cap * (1-p2cap)/n2)

SE = sqrt(0.8056 * (1-0.8056)/144 + 0.2143*(1-0.2143)/154)

SE = 0.0467

For 0.98 CI, z-value = 2.33

Confidence Interval,

CI = (p1cap - p2cap - z*SE, p1cap - p2cap + z*SE)

CI = (0.8056 - 0.2143 - 2.33*0.0467, 0.8056 - 0.2143 +
2.33*0.0467)

CI = (0.4825 , 0.7001)

b)

yes, the treatement is effective as the difference in two
proportion is significant

In a study of treatments for very painful "cluster" headaches,
154 patients were treated with oxygen and 155 other patients were
given a placebo consisting of ordinary air. Among the 154 patients
in the oxygen treatment group, 114 were free from headaches 15
minutes after treatment. Among the 155 patients given the placebo,
30 were free from headaches 15 minutes after treatment. Use a 0.05
significance level to test the claim that the oxygen treatment is
effective. Find the test...

In a study of treatments for very painful "cluster" headaches,
144 patients were treated with oxygen and 153 other patients were
given a placebo consisting of ordinary air. Among the 144 patients
in the oxygen treatment group, 117 were free from headaches 15
minutes after treatment. Among the 153 patients given the placebo,
35 were free from headaches 15 minutes after treatment. Use a 0.05
significance level to test the claim that the oxygen treatment is
effective. Complete parts (a)...

In a study of treatments for very painful "cluster" headaches,
147 patients were treated with oxygen and 148 other patients were
given a placebo consisting of ordinary air. Among the 147 patients
in the oxygen treatment group, 114 were free from headaches 15
minutes after treatment. Among the148 patients given theplacebo,
23 were free from headaches 15 minutes after treatment. Use a 0.05
significance level to test the claim that oxygen treatment is
effective. Complete parts (a) through (c) below....

In
a study of treatments for very painful "cluster" headaches, 152
patients were treated with oxygen and 148 other patients were given
a placebo consisting of ordinary air. Among the 152, patients in
the oxygen treatment group, 108were free from headaches 15 minutes
after treatment. Among the 148patients given the placebo, 24were
free from headaches 15 minutes after treatment. Use a 0.05
significance level to test the claim that the oxygen treatment is
effective.

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