In a study of treatments for very painful cluster\" headaches, 159 patients were

Question

In a study of treatments for very painful cluster" headaches, 159 patients were treated with oxygen and 150 other patients were given a placebo consisting of ordinary air. Among the 159 patients in the oxygen treatment group, 106 were free from headaches 15 minutes after treatment. Among the 150 patients given the placebo, 37 were free from headaches 15 minutes after treatment Use a 0.01 significance level to test the claim that the oxygen treatment is effective. Complete parts (a) through (c) belovw a. Test the claim using a hypothesis test. Consider the first sample to be the sample of patients treated with oxygen and the second sample to be the sample of patients given a placebo. What are the null and alternative hypotheses for the hypothesis test? B. Ho:P1=P2 H1: P1 P2 F. Ho P1 P2 Identify the test statistic. Round to two decimal places as needed.)

Explanation / Answer

The statistical software output for this problem is:

Two sample proportion summary hypothesis test:
p1 : proportion of successes for population 1
p2 : proportion of successes for population 2
p1 - p2 : Difference in proportions
H0 : p1 - p2 = 0
HA : p1 - p2 > 0

Hypothesis test results:

Hence,

Test statistic

z = 7.40

Difference Count1 Total1 Count2 Total2 Sample Diff. Std. Err. Z-Stat P-value p1 - p2 106 159 37 150 0.42 0.056754282 7.4003227 <0.0001

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