Question

In a study of treatments for very painful​ "cluster" headaches,

159159

patients were treated with oxygen and

154154

other patients were given a placebo consisting of ordinary air. Among the

159159

patients in the oxygen treatment​ group,

111111

were free from headaches 15 minutes after treatment. Among the

154154

patients given the​ placebo,

3434

were free from headaches 15 minutes after treatment. Use a

0.050.05

significance level to test the claim that the oxygen treatment is effective. Complete parts​ (a) through​(c) below.

Answer 1

p1 = 111/159 = 0.6981   Sample Proportion of oxygen treatment group free from headache       
n1 = 159   Sample size of oxygen treatment group       
p2 = 34/154 = 0.2208   Sample Proportion of placebo treatment group free from headache       
n2 = 154   Sample size of placebo treatment group       
          
the null and alternative hypothesis are           
Ho : p1 = p2          
H1 : p1 > p2                          Whether oxygen treatment is effective than placebo treatment       
          
This is a one sided right tailed test          
Let α = 0.05                       Level of significance        
Finding the Standard error          
We find the pooled proportion          

p̂ = 0.4633                       Pooled proportion       

Standard Error (SE) = 0.056378          

    where pdiff = 0 since null hypothesis states  p1 = p2      

Zcalc = 8.4661          
          
p-value          
We find p-value such that           
p-value = P(Z > 8.4661)          
We find p-value using z-tables or the Excel function NORM.S.DIST          
p-value = 1 - NORM.S.DIST(8.4661, TRUE)          
p-value = 1 - 1          
p-value = 0          
          
Decision
0 < 0.05          
p-value < α          
Hence we reject the null hypothesis          

Conclusion           
Ho is rejected          
Interpretation :          
There exists enough statistical evidence to show that           
proportion of patients free from headaches given oxygen treatment is more than those given placebo          
That is the oxygen treatment is effective.