Question

# Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final...

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?

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

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