Researchers gave 20 index cards to a waitress at an Italian restaurant in New Jersey. Before delivering the bill to each customer, the waitress randomly selected a card and wrote on the bill the same message that was printed on the index card. 20 of the cards had the message "The weather is supposed to be really good tomorrow. I hope you enjoy the day!" Another 20 cards contained the message "The weather is supposed to be not so good tomorrow. I hope you enjoy the day anyway!" After the customers left, the waitress recorded the amount of the tip (percent of bill) before taxes. Here are the tips for those receiving the good-weather message:

The tips for the 20 customers who received the bad- weather message are

Give a 95% confidence interval for the difference between the mean percent tips for the two different messages.
Define the point estimate (x-bar minus y-bar) to be the good weather mean minus the bad weather mean.

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