One Sample Hypothesis   Tips
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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.