Researchers gave 40 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. twenty 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: 20.8 18.8 20.3 20.9 22.2 23.5 23.2 25.1 22.6 20.4 25.2 22.6 27.4 20.7 22.2 24.5 21.4 22.4 22.4 22.7 the tips for the 20 customers who received the bad-weather message are listed here 18.4 19.3 19.6 19.3 18.9 19.4 18.7 16.6 17.0 14.0 17.4 14.0 17.8 20.5 20.4 19.0 18.2 23.3 18.6 19.5 (a) what degrees of freedom would you use in the conservative two-sample t procedures to compare the lack-of-control and in-control groups? what is the two-sample t test statistic? (round your answer to three decimal places.) t- (b) is there good evidence that the two different messages produce different percent tips? report your conclusions. (assume a 95% confidence level.) there is strong evidence that the mean tip percentage differs between the two types of forecasts presented to patrons. there is not enough evidence to conclude that the mean tip percentage differs between the two types of forecasts presented to patrons. you may need to use the appropriate appendix table to answer this question.