Question

Donz 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)   Donz 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)   Donz 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) Donz 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.

Answer 1

a. Donz wish to test the difference in mean sales before and after the change. Thus the samples are dependent. The test is paired t test for significance of mean difference. Test for paired difference

b. In this case one can test whether the population mean rating given by people is equal to specific value or greater/less than specific value. Test for population mean i.e t test for one population

c. On the basis of data collected in this case test for proportion of positive rating/ negative rating to new menu can be performed. Test for population proportion for one population.

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