Question

In a study of treatments for very painful​ "cluster" headaches, 144 patients were treated with oxygen and 153 other patients were given a placebo consisting of ordinary air. Among the 144 patients in the oxygen treatment​ group, 117 were free from headaches 15 minutes after treatment. Among the 153 patients given the​ placebo, 35 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.

Answer 1

Sample 1 : For oxygen group : n1=144 , X1=117

Sample 2 : For placebo group : n2=153 , X2=35

The estimate of the sample proportion is ,

The pooled estimate is ,

The null and alternative hypothesis is ,

(Claim)

The test is one-tailed test.

The test statistic is ,

The critical value is , ; From Z-table

The rejection rule is , reject Ho , if Z-stat>1.64

Decision rule : Here , Z-stat=10.06>1.64

Therefore , reject Ho.

Conclusion : There is sufficient evidence to support the claim that the oxygen treatment is effective.