Do two landing pages really convert at different rates?

Question

A marketing team runs two landing pages. Page A gets 1200 visitors and 84 sign-ups (7.0%); page B gets 1200 visitors and 120 sign-ups (10.0%).

Test at the 5% level (two-sided) whether the two true conversion 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 = 84/1200 = 0.070 and \hat pB = 120/1200 = 0.100. Under H0 the two rates are equal, so pool them: \hat p = \frac{84 + 120}{1200 + 1200} = \frac{204}{2400} = 0.085. Standard error of the difference under the null: 	ext{SE} = \sqrt{\hat p (1-\hat p)\left(\frac{1}{nA} + \frac{1}{nB}ight)} = \sqrt{0.085 	imes 0.915 	imes \left(\frac{2}{1200}ight)} = \sqrt{0.00012963} = 0.01139. Test statistic: z = \frac{\hat pB - \hat pA}{	ext{SE}} = \frac{0.100 - 0.070}{0.01139} = \frac{0.030}{0.01139} = 2.64. Since 2.64 1.96, rej…

Do two landing pages really convert at different rates?

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