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.
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 ,
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.
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