Do two email subject lines get different open rates?

Question

An email campaign tests two subject lines. Version 1 is sent to 2000 recipients and opened by 640 (32%); version 2 is sent to 2000 recipients and opened by 700 (35%).

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

Accepted Answer

Hypotheses: H0: p1 = p2 versus H1: p1 
eq p2. Sample proportions: \hat p1 = 640/2000 = 0.320, \hat p2 = 700/2000 = 0.350. Pooled proportion: \hat p = \frac{640 + 700}{2000 + 2000} = \frac{1340}{4000} = 0.335. Standard error under the null: 	ext{SE} = \sqrt{0.335 	imes 0.665 	imes \left(\frac{2}{2000}ight)} = \sqrt{0.222775 	imes 0.001} = \sqrt{0.000222775} = 0.01493. Test statistic: z = \frac{0.350 - 0.320}{0.01493} = \frac{0.030}{0.01493} = 2.01. Since 2.01 1.96, reject H0 (just barely). The two-sided p-value is about 0.044. Conclusion: version 2 has a significantly higher open rate. …

Do two email subject lines get different open rates?

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