1. TIPS
1SHT
By:
Philip Russin
Chris Generose

2. General Procedure for
Hypothesis Testing
1. Define the Hypothesis
• Null & Alternative
2. Calculate the Test Statistic
• Using Z-tests or T-tests
• Observed vs. Critical values
• Significance Level (p-value vs. alpha-level)
3. Make a Decision (using rules of thumb, or
decision rules)
• Decision rules are based on comparing the data to
statistical thresholds

3. Define the Hypothesis
 First step in hypothesis testing is to translate the research
questions into hypotheses.
 Every statistical test tests the Null hypothesis against the
Alternative hypothesis
 Null Hypothesis: States the obvious; status quo
• Should use the equality sign
 Alternative Hypothesis: Bears the burden of proof
• Includes the remainder of the population that is not covered by the
null
 One-tailed vs. Two-tailed Tests

4. Calculate the Test Statistic
 Observed, Critical, & Significance Level
 If the sample mean is close to the
assumed population mean, ACCEPT the
null hypothesis
 If the sample mean is far from the
assumed population mean, REJECT the
null hypothesis.

5. Make a Decision
 Based on statistical thresholds:
• /OBS/ < CRIT – Accept Null
• /OBS/ > CRIT – Reject Null
• P-value < Alpha-level = Reject Null
• P-value > Alpha-level = Accept Null
 Form a conclusion
 Make a recommendation

6. Case Overview
 Food servers’ tips in restaurants may be influenced by
many factors:
 The nature of the restaurant
 Size of the party
 Table location in the restaurant
 Etc.
 To make appropriate assignments for the food
servers, restaurant managers need to know what these
factors are.
 Must avoid unfair treatment of the food servers, for whom
the tips are a major component of pay.

7. Case Overview (cont.)
 Based on one food server’s data about all customers over a
two and a half month period
 The data was recorded on those days and during times when
the food server was routinely assigned to work.
 The following information was recorded:
 The amount of the total bill
 The amount of the tip
 The gender
 Smoker vs. Non
 The day of the week (3=Thu, 4=Fri, 5=Sat, 6=Sun)
 Time of day (day, night)
 Size of the party (1-6)
 Case Question: Based on this data, what are your
recommendations to avoid unfair treatment of the food
servers?

8. Summary Measures
 245 Total Observations
 Average Total Bill: $19.79
 Mean Tip: $3.00 or 15.2%
 Average Party Size: 2.5
 Mean Tip by Shift: $2.73 (Day) & $3.10 (Night)
 68 Day & 176 Night Shifts
 Mean Tip of Males: $3.09
 Mean Tip of Females: $2.83
 151 Non-Smokers ($2.99) & 93 Smokers ($3.01)

9. Mean Tip per Day
Average of Tip
3.30
3.20
3.10
3.00
2.90 Drop Series Fields Here
2.80 Total
2.70
2.60
2.50
2.40
Thurs. Fri. Sat. Sun.
Day

10. Mean Tip by Party Size
Average of Tip
6.00
5.00
4.00
Drop Series Fields Here
3.00
Total
2.00
1.00
0.00
1 2 3 4 5 6
SizeOfParty

11. Mean Tip by Size of Party & Shift
Average of Tip
6
5
4 TimeOfDay
SizeOfParty
Night
3
Day
2
1
0.00 2.00 4.00 6.00

12. Mean Tip by Size of Party & Day
Average of Tip
6.00
5.00
4.00 Day
Thurs.
3.00 Fri.
2.00 Sat.
Sun.
1.00
0.00
1 2 3 4 5 6
SizeOfParty

13. Hypothesis Test 1
 Question: Are Saturdays & Sundays the best days for
tips?
 Null: Saturday & Sunday ARE the best days for tips.
 Alt: Saturday & Sunday are NOT the best days for tips.
 Hypothesized Value: $3.00
 Sample Size: 163
 Only 81 Thursdays & Fridays
 Sample Mean: $3.12
 One – Tailed Test

14. Hypothesis Test 1 (cont.)
 Test Statistic (OBS) = 1.007
 Critical Measure = 1.645
 /OBS/ > Crit? = NO
 P-value = 0.157
 Alpha-level = 0.05
 P-value < Alpha? = NO
 ACCEPT NULL!!!
 Conclusion: Saturday & Sunday ARE the best days for
tips.
 Average tip for Thursday & Friday is $2.76

15. Hypothesis Test 2
 Question: Do smaller parties tip better than average?
 Null: Smaller parties DO tip better.
 Alt: Smaller parties do NOT tip better.
 Hypothesized Value: $3.00
 Sample Size: 198 (sizes 1-3)
 Only 46 Large Parties (sizes 4-6)
 Sample Mean: $2.71
 One – Tailed Test

16. Hypothesis Test 2 (cont.)
 Test Statistic (OBS) = (3.442)
 Critical Measure = 1.645
 /OBS/ > Crit? = YES
 P-value = 0.000
 Alpha-level = 0.05
 P-value < Alpha? = YES
 REJECT NULL!!!
 Conclusion: Smaller parties do NOT tip better.
 Large parties average tip is $4.22

17. Conclusion
 Males tip better than Females
 Saturdays & Sundays are the best days for
tips.
 Large Parties tip better than smaller
parties, although there are many more
smaller parties.
 Night Shift usually gets better tips

18. Recommendation
 Schedule food servers on an alternating week to
week routine based on day and shift:
 Days 3 & 5 (Thursday & Saturday)
• Mean tip $2.88
 Days 4 & 6 (Friday & Sunday)
• Mean tip $2.99
 All servers will also alternate Day & Night
shifts for equal opportunity.