Question

In a study of treatments for very painful​ "cluster" headaches, 141 patients were treated with oxygen and 150 other patients were given a placebo consisting of ordinary air. Among the 141

patients in the oxygen treatment​ group, 119 were free from headaches 15 minutes after treatment. Among the 150 patients given the​ placebo, 20 were free from headaches 15 minutes after treatment. Use a 0.05 significance level to test the claim that the oxygen treatment is effective.

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

The 90​% confidence interval is???

______<(p1-p2)<_______?

​(Round to three decimal places as​ needed.)

B. What is the conclusion based on the confidence​ interval? Because the confidence interval limits INCLUDE/ DONT INCLUDE ​0, it appears that the two cure rates are NOT EQUAL/ EQUAL.

Because the confidence interval limits include ONLY POSITIVE/ ONLY NEGATIVE/ POSITIVE AND NEGATIVE, ​values, it appears that the cure rate is HIGHER/ LOWER/ THE SAME, for the oxygen treatment than for the placebo.

(answer the parts in bold)

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 not effective in curing​ "cluster" headaches because the cure rates appear to be the same

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

D.The results are inconclusive.

Answer 1

We need to construct the 95% confidence interval for the difference between population proportions ​. We have been provided with the following information about the sample proportions:

The sample proportion 1 is computed as follows, based on the sample size N1​=141 and the number of favorable cases X1​=119:

The sample proportion 2 is computed as follows, based on the sample size N2​=150 and the number of favorable cases X2​=20:

The critical value for α=0.05 is . The corresponding confidence interval is computed as shown below:

Therefore, based on the data provided, the 95% confidence interval for the difference between the population proportions is 0.63<p<0.792, which indicates that we are 95% confident that the true difference between population proportions is contained by the interval (0.63,0.792)

B.

Because the confidence interval limits DONT INCLUDE ​0, it appears that the two cure rates are NOT EQUAL.

Because the confidence interval limits include ONLY POSITIVE, ​values, it appears that the cure rate is HIGHER for the oxygen treatment than for the placebo.

C.

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

Please let me know if anything is unclear in comments. Will reply ASAP. Please upvote if satisfied!