Does one vaccine batch cause more side effects?

Question

Two batches of a vaccine are compared. In group A, 18 of 300 people report a side effect (6%); in group B, 36 of 300 report one (12%).

Test at the 5% level (two-sided) whether the true side-effect rates differ, using a pooled two-proportion z-test, and report the z-statistic.

Accepted Answer

Hypotheses: H0: pA = pB versus H1: pA 
eq pB. Sample proportions: \hat pA = 18/300 = 0.060, \hat pB = 36/300 = 0.120. Pooled proportion: \hat p = \frac{18 + 36}{300 + 300} = \frac{54}{600} = 0.090. Standard error under the null: 	ext{SE} = \sqrt{0.090 	imes 0.910 	imes \left(\frac{2}{300}ight)} = \sqrt{0.0819 	imes 0.0066667} = \sqrt{0.000546} = 0.02337. Test statistic: z = \frac{0.120 - 0.060}{0.02337} = \frac{0.060}{0.02337} = 2.57. Since 2.57 1.96, reject H0. The two-sided p-value is about 0.010. Conclusion: group B has a significantly higher side-effect rate. Takeaway. When one rat…

Does one vaccine batch cause more side effects?

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