Question

In a study of treatments for very painful​ "cluster" headaches, 152 patients were treated with oxygen and 145 other patients were given a placebo consisting of ordinary air. Among the 152 patients in the oxygen treatment​ group, 115 were free from headaches 15 minutes after treatment. Among the 145 patients given the​ placebo, 31 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) through​ (c) below.

a. 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?

Identify the test statistic.

z = ____ (Round to two decimal points as needed.)

Identify the​ P-value.

P-value = ____ (Round to three decimal points as needed.)

What is the conclusion based on the hypothesis​ test?

The​ P-value is (less than or greater than) the significance level of α = 0.05​, so (fail to reject or reject) the null hypothesis. There (is sufficient or is not sufficient) evidence to support the claim that the cure rate with oxygen treatment is higher than the cure rate for those given a placebo.

b. Test the claim by constructing an appropriate confidence interval.

The 90​% 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 or do not include) 0, it appears that the two cure rates are (not equal or equal.) Because the confidence interval limits include (only negative or positive and negative or only positive) values, it appears that the cure rate is (higher or the same or lower) for the oxygen treatment than for the placebo.

c. 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 rate for the oxygen treatment appears to be lower than that of the placebo.

B. The results suggest that the oxygen treatment is effective in curing​ "cluster" headaches.

C. The results suggest that the oxygen treatment is not effective in curing​ "cluster" headaches because the cure rates appear to be the same.

D. The results are inconclusive.

Answer 1

a)

from above z =9.35

p value =0.000

The​ P-value is less than the significance level of α = 0.05​, so we reject the null hypothesis. There 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.

b)

90​% confidence interval is 0.462 < p1-p2 <0.623

Because the confidence interval limits do not include 0, it appears that the two cure rates are not equal Because the confidence interval limits include positive values, it appears that the cure rate is higher for the oxygen treatment than for the placebo.

c)

B. The results suggest that the oxygen treatment is effective in curing​ "cluster" headaches.