A study of tipping behaviors examined the relationship between the color of the shirt worm by the server and whether or not the customer left a tip. There were 418 male customers in the study; 40 of the 69 who were served by a server wearing a red shirt left a tip. Of the 349 who were served by a server wearing a different colored shirt, 130 left a tip.

a. find the large-sample 95% confidence interval for the difference in proportions and use the scenario to explain the meaning of the confidence interval.
b. perform the large-sample significance test and use the scenario to explain the meaning of the significance test.