Steven Solomon, the owner of Leonardo\'s Italian Restaurant, wonders whether red

Question

Steven Solomon, the owner of Leonardo's Italian Restaurant, wonders whether redesigned menus will increase, on the average, the amount that customers spend in the restaurant. For the following scenarios pick a statistical method from this chapter that would be appropriate for analyzing the data, indicating whether the samples are independent or dependent, which parameter is relevant and what inference method you would use: a. Solomon 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. Solomon randomly samples 100 people and shows them each both menus, asking them to give a rating between 0 and 10 for each menu. c. Solomon randomly samples 100 people and shows them each both menus, asking them to give an overall rating of "positive" or "negative" to each menu. d. Solomon randomly samples 100 people and randomly separates them into two groups of 50 each. He asks those in group 1 to give a rating to the old menu and those in group 2 to give a rating to the new menu, using a 0 to 10 rating scale.

Explanation / Answer

a. Solomon records the mean sales the week before the change and the week after the change and then wonders whether the difference is "statistically significant."

We will use 2 sample parametric t-test to test the difference between 2 samples. It will be 1 tailed (right tailed t test)

H0: after_sales<=before_sales

Ha: after_sales>before_sales

b. Solomon randomly samples 100 people and shows them each both menus, asking them to give a rating between 0 and 10 for each menu.

Since data will be ordinal so Normality cant be expected. We will use Wilcoxon non-parametric U test with above hypothesis.

c. Solomon randomly samples 100 people and shows them each both menus, asking them to give an overall rating of "positive" or "negative" to each menu.

We will test the proportion of positive responses with negative ones using Z-proportion test.

H0: positive proportion for new menu <=positive proportion for old menu

Ha: positive proportion for new menu >positive proportion for old menu

d. wilcoxon test

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