7.32 Happy face: interaction. Researchers at Temple University wanted to know the following: If you work waiting tables and you draw a happy face on the back of your customers' checks, will you get better tips? To study this question, they enlisted the cooperation of two servers at a Philadelphia restaurant. One was male, the other female. Each server recorded his or her tips for their next 50 tables. For 25 of the 50, following a predetermined randomization, they drew a happy face on the back of the check. The other 25 randomly chosen checks got no happy face. The response was the tip, expressed as a percentage of the total bill. The averages for the male server were 18% with a happy face, 21% with none. For the female server, the averages were 33% with a happy face, 28% with none.

a. Regard the dataset as a two-way ANOVA, which is the way it was analyzed in the article. Name the two factors of interest, tell whether each is observational or experimental, and identify the number of levels.

b. Draw an interaction graph(use R). Is there evidence of interaction? Describe the pattern in words, using the fact that an interaction, if present, is a difference of differences.

(Please include R the code of graph)