In a study of treatments for very painful "cluster" headaches, 140 patients were treated with oxygen and 158 other patients were given a placebo consisting of ordinary air. Among the 140 patients in the oxygen treatment group, 113 were free from headaches 15 minutes after treatment. Among the 158 patients given the placebo, 35 were free from headaches 15 minutes after treatment. Use a significance level to test the claim that the oxygen treatment is effective. A) Find test statistic z B) Find the P-value C) Construct the appropriate confidence interval D) determine if the oxygen treatment is effective

A

B

C

D

  The  oxygen treatment  is effective because

1 the is no 0 in the interval telling us that the treatments are different

 2 the upper and the lower limit are positive tell us that the proportion of those treated by the oxygen treatment is greater

Step-by-step explanation:

From the question we are told that

    The  first sample size is  

     The  number of patient which the oxygen cured is k = 113  

     The second sample size is  

     The number of patient that  placebo cured is  l =  35

The first sample proportion is

The second sample proportion is  

The null hypothesis is  

 The  alternative hypothesis is  

Let assume the level of significance be

Generally the pooled proportion is mathematically evaluated as

substituting values

Generally the standard error is mathematically represented

      substituting values

Generally the test statistics is mathematically represented as

The  p-value is from the normal distribution table as  

given that the null hypothesis is rejected

From the normal distribution table the critical value of    is  

Generally the margin of error is mathematically the represented as

The 95% confidence interval is mathematically  represented as

substituting value

The  oxygen treatment  is effective because

1 the is no 0 in the interval telling us that the treatments are different

 2 the upper and the lower limit are positive tell us that the proportion of those treated by the oxygen treatment is greater

d

step-by-step explanation: