# Elementary statistics case study | Mathematics homework help

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Case Study 1: Restaurant Tipping

Context

A food server’s tip in restaurants may be influenced by many factors including the nature of the restaurant, size of the party, and table locations in the restaurant. To make appropriate assignments (e.g. which tables the food server waits on) for the food servers, restaurant managers need to know what these factors are. For the sake of staff morale they must avoid either the substance or appearance of unfair treatment of the food servers, for whom tips are a major component of pay. In one restaurant, a food server recorded the following data on all customers served during an interval of two and a half months. The restaurant was one of a national chain and served a varied menu.  In observance of local law the restaurant offered seating in a non-smoking sections to patrons who requested it. The data was assigned to those days and during those times when the food server was routinely assigned to work.

Data Description

TOTBILL:           Total bill, including tax, in dollars

TIP:                     Tip in dollars

GENDER:           Gender of person paying the bill  (female, male)

SMOKER:           Smoker in the group? (no, yes)

DAY:                   Thursday, Friday, Saturday, Sunday

TIME:                 Lunch or dinner

SIZE:                   Size of the group

TIPRATE:          Create this variable (TIPRATE=TIP/TOTBILL)

The data is available on Blackboard Case Studies tab as a JMP file and an EXCEL file.

(1) Does the data collection procedure represent an experimental design or an
observational study design?

(2) Create another variable: TIPRATE = TIP/TOTBILL

(3) What is the number of cases (records, entities, observations) in the dataset?

(4) How many variables are in the dataset?

(5) Classify each variable as either Categorical or Quantitative.
(6) Fill all blank cells in Table 1.

 Table 1 TOTBILL TIP TIPRATE SIZE Mean Standard Deviation Median Coefficient of Variation

(7) Fill all blank cells in Table 2 with values (counts) for the gender of bill payers and whether there is a smoker or not in the group.

 Table 2 Gender/Smoker No Yes Total Male Female Total

(8) Fill all blank cells in Table 3 with percentages – e.g. for the first row with blank cells – the number of males who paid the bill who were non-smokers as a percentage of the total number of observations in the sample; the number of males who paid the bill who were smokers as a percentage of the total number of observations in the sample; the total number of males as a percentage of the total number of observations in the sample. Similar approach for females who paid the bill, as well as for smoker or non-smoker (for all calculations the denominator is always the total number of observations in the sample).

 Table 3 Gender/Smoker No Yes Total Male Female Total

(9) Fill all blank cells in Table 4 with values (counts) for the time of day (lunch, dinner) and day of the week.

 Table 4 Time/Day Thursday Friday Saturday Sunday Lunch Dinner Total

(10) Construct a box plot for the TIPRATE.  (Copy and paste your boxplot in this document). What does it indicate about the shape of the distribution of the TIP RATE data?

(11) Construct a histogram for TIP. (Copy and paste the histogram in this document). What does it indicate about the shape of the distribution of the TIP data?

(12) Which of the other quantitative variables is most highly correlated with the TIPRATE?

(13) What is the relationship between tips (TIP) and the total bill (TOTBILL)?

(14) In which instance is the variation greater – (a) tips given by groups with a smoker or tips given by non-smoking groups?

(15) What does the evidence indicate? Is there a tendency for customers to give “generous” or “cheap” tips relative to the total bill?

(16) Construct a Mosaic plot of the variables: GENDER of the bill payer and DAY (days of the week. What does the Mosaic Plot indicate?

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