# 8. In a study of treatments fo

8. In a study of treatments for very painful “cluster”headaches, 153 patients were treated with oxygen and 147 otherpatients were given a placebo consisting of ordinary air. Among the153 patients in the oxygen treatment group, 120 were free fromheadaches 15 minutes after treatment. Among the 147 patients giventhe placebo, 29 were free from headaches 15 minutes aftertreatment. Use a 0.05 significance level to test the claim that theoxygen 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 treatedwith oxygen and the second sample to be the sample of patientsgiven a placebo. What are the null and alternative hypotheses forthe 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 levelof a= 0.05, so (reject/fail to reject) the null hypothesis. There(is sufficient/is not sufficient) evidence to support the claimthat the cure rate with oxygen treatment is higher than the curerate for those given a placebo.

b. Test the claim by constructing an appropriate confidenceinterval.

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 notinclude

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

(lower/higher/the same) for the oxygen treatment than for theplacebo.

c. Based on the results, is the oxygen treatmenteffective?

A.The results suggest that the oxygen treatment is effective incuring “cluster” headaches.

B.The results suggest that the oxygen treatment is not effectivein curing “cluster” headaches because the cure rates appear to bethe same.

C.The results suggest that the oxygen treatment is not effectivein curing “cluster” headaches because the cure rate for the oxygentreatment appears to be lower than that of the placebo.

D.The results are inconclusive.

Answer:

**Given:**

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

**first group** is patients were treated withoxygen and

**second group** is patients were given a placeboconsisting of ordinary air

**a)**

**ANSWER: C**

**Hypothesis:**

Ho: P1 = P2

Ha: P1 > P2 Or The cure rate with oxygen treatment is higherthan 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 significancelevel of = 0.05, so**reject** the null hypothesis. There is**sufficient** evidence to support the claim that thecure rate with oxygen treatment is higher than the cure rate forthose 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 notinclude** 0, it appears that the two cure rates are**not equal** Because the confidence interval limitsinclude **only positive** values, it appears that thecure rate is **higher** for the oxygen treatment thanfor the placebo.

C)

**ANSWER:**

**A.The results suggest that the oxygen treatment iseffective in curing “cluster” headaches.**