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One Sample Hypothesis - Tips
 

One Sample Hypothesis - Tips

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    One Sample Hypothesis - Tips One Sample Hypothesis - Tips Presentation Transcript

    • TIPS 1SHT By: Philip Russin Chris Generose
    • 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
    • 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
    • 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.
    • 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
    • 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.
    • 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?
    • 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)
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    • 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
    • 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
    • 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
    • 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
    • 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
    • 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.