The document outlines the general procedure for hypothesis testing, including defining the null and alternative hypotheses, calculating the test statistic, and making a decision based on significance levels and critical values. It then provides an example case study analyzing factors that may influence food servers' tips, such as day of week, party size, gender, and time of shift. Two hypothesis tests are conducted. The first finds Saturday and Sunday are the best days for tips. The second finds that larger parties tip better than smaller parties, on average. Based on the results, the recommendation is to schedule food servers on a rotating basis across days and shifts to ensure fair treatment.

1. TIPS 1SHT By: Philip Russin Chris Generose

2. General Procedure for Hypothesis Testing Define the Hypothesis Null & Alternative Calculate the Test Statistic Using Z-tests or T-tests Observed vs. Critical values Significance Level (p-value vs. alpha-level) 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)

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.