Question: Mark has been working as a doorman at two different buildings in White Plains: Building A and Building B. Over time, Mark has come to believe that the residents of Building A are more "generous" than the residents of Building B (generous means that they give a Christmas bonus tip of at least $40 to be split among the doormen). He takes a simple random sample of 30 residents of building A and finds that 26 of them were generous in 2007. He also takes a simple random sample of 37 residents of building B; 19 of them were generous in 2007. Construct a 95% confidence interval for the difference between the two proportions; based on this interval, does Mark have evidence showing that the residents of building A are more generous than the residents of building B?

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