Dave Hughes owns a local restaurant. He wonders if a redesign of the menu will increase, on average, the amount customers spend when visiting his establishment. For the following scenarios, pick a statistical method we discussed regarding comparing two groups that would be appropriate for analyzing the problem. Indicate whether the samples would be dependent or independent, which parameter(s) is(are) relevant, and what inference method you would use.

a)(5 points) Hughes records the mean sales the week before the change and the week after the change and then wonders whether the difference is statistically significant.

b)(5 points) Hughes randomly samples 100 people and shows both menus to each person, asking them to rate each menu from 0 (very poor) to 20 (excellent).

c)(5 points) Hughes randomly samples 100 people and randomly separates them into two groups of 50. He asks those in group 1 to give a rating of 'positive' or 'negative' to the old menu and those in group 2 to give a rating of 'positive' or 'negative' to the new menu.