Question

8. In a study of treatments for very painful​ "cluster" headaches, 153 patients were treated with oxygen and 147 other patients were given a placebo consisting of ordinary air. Among the 153 patients in the oxygen treatment​ group, 120 were free from headaches 15 minutes after treatment. Among the 147 patients given the​ placebo, 29 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?

A.H 0​: p 1 ≤ p 2

H 1​: p 1 ≠ p 2

B. H 0​: p 1 = p 2

H 1​: p 1 ≠ p 2

C.H 0​: p 1 = p 2

H 1​: p 1 > p 2

D. H 0​: p 1 ≠p 2

H 1​: p 1= p 2

E.H 0​: p 1 = p 2

H 1​: p 1 < p 2

F. H 0​: p 1 ≥ p 2

H 1​: p 1 ≠ p 2

Identify the test statistic.

Z=___

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

Identify the​ P-value.

​P-value=

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

What is the conclusion based on the hypothesis​ test?

The​ P-value is (greater than/less than) the significance level of a= 0.05​, so (reject/fail to reject) the null hypothesis. There (is sufficient/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/do not include

​0, it appears that the two cure rates are (equal/not equal.) Because the confidence interval limits include (positive and negative/only positive/only negative) ​values, it appears that the cure rate is

(lower/higher/the same) 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 effective in curing​ "cluster" headaches.

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 not effective in curing​ "cluster" headaches because the cure rate for the oxygen treatment appears to be lower than that of the placebo.

D.The results are inconclusive.

Answer 1

Given:

n1=153 , X1=120, n2=147, X2=29,

first group is patients were treated with oxygen and

second group is patients were given a placebo consisting of ordinary air

a)

ANSWER: C

Hypothesis:

Ho: P1 = P2

Ha: P1 > P2 Or The cure rate with oxygen treatment is higher than the cure rate for those given a placebo

b)

Q = 1 - P = 1 - 0.497 = 0.503

Test statistic:

P-value: 0.00001

The​ P-value is less than the significance level of = 0.05​, so 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:

Critical value:

Z _/2 = Z _0.10/2 = 1.645

90% Confidence interval:

(0.510, 0.664)

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 only positive ​values, it appears that the cure rate is higher for the oxygen treatment than for the placebo.

C)

ANSWER:

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