10.12 Obama A/B testing To increase Barack Obama’s visibility and to raise money for the campaign leading up to the 2008 presidential election, Obama’s analytics team conducted an A/B test with his website. In the original version, the button to join the campaign read “Sign Up”.

In an alternative version, it read “Learn More”. Of 77,858 visitors to the original version, 5851 clicked the button. Of 77,729 visitors to the alternative version, 6927 clicked the button. Is there evidence that one version was more successful than the other in recruiting campaign members?

a. Sketch an appropriate graph to compare the sample proportions visually.

b. Show all steps of a significance test, using the computer output. Define any parameters you are using when specifying the hypotheses. Mention whether there is a significant difference at the 0.05 significance level.

c. Interpret the confidence interval shown in the output.
Why is this interval more informative than just reporting the P-value?

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Sample SignUp Learn More X N Sample p 77858 5851 0.075150 77729 6927 0.089117 - Difference = p(SignUp) p (Learn More) Estimate for difference: -0.013968 95% CI for difference: (-0.016695, -0.011239) Test for difference = 0 (vs 0): Z = 10.03 P-Value = 0.000