The statistical software output for this problem is:
Two sample proportion summary hypothesis
test:
p_{1} : proportion of successes for population 1
p_{2} : proportion of successes for population 2
p_{1} - p_{2} : Difference in proportions
H_{0} : p_{1} - p_{2} = 0
H_{A} : p_{1} - p_{2} ≠ 0
Hypothesis test results:
Difference | Count1 | Total1 | Count2 | Total2 | Sample Diff. | Std. Err. | Z-Stat | P-value |
---|---|---|---|---|---|---|---|---|
p_{1} - p_{2} | 561 | 4908 | 492 | 4899 | 0.01387452 | 0.0062523513 | 2.2190883 | 0.0265 |
Hence,
Ho: p_{treatment} = p_{placebo}
Ha: p_{treatment} p_{placebo}
z = 2.22
P - value = 0.0265
Conclusion: Option B is correct.
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