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# One Sample Hypothesis - Tips

## on Mar 24, 2010

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## One Sample Hypothesis - TipsPresentation 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.