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One Sample Hypothesis Tips


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One Sample Hypothesis Tips

  1. 1. TIPS 1SHT By: Philip Russin Chris Generose
  2. 2. General Procedure for Hypothesis Testing <ul><li>Define the Hypothesis </li></ul><ul><ul><ul><li>Null & Alternative </li></ul></ul></ul><ul><li>Calculate the Test Statistic </li></ul><ul><ul><ul><li>Using Z-tests or T-tests </li></ul></ul></ul><ul><ul><ul><li>Observed vs. Critical values </li></ul></ul></ul><ul><ul><ul><li>Significance Level (p-value vs. alpha-level) </li></ul></ul></ul><ul><li>Make a Decision (using rules of thumb, or decision rules) </li></ul><ul><ul><ul><li>Decision rules are based on comparing the data to statistical thresholds </li></ul></ul></ul>
  3. 3. Define the Hypothesis <ul><li>First step in hypothesis testing is to translate the research questions into hypotheses. </li></ul><ul><li>Every statistical test tests the Null hypothesis against the Alternative hypothesis </li></ul><ul><li>Null Hypothesis: States the obvious; status quo </li></ul><ul><ul><ul><li>Should use the equality sign </li></ul></ul></ul><ul><li>Alternative Hypothesis: Bears the burden of proof </li></ul><ul><ul><ul><li>Includes the remainder of the population that is not covered by the null </li></ul></ul></ul><ul><li>One-tailed vs. Two-tailed Tests </li></ul>
  4. 4. Calculate the Test Statistic <ul><li>Observed, Critical, & Significance Level </li></ul><ul><li>If the sample mean is close to the assumed population mean, ACCEPT the null hypothesis </li></ul><ul><li>If the sample mean is far from the assumed population mean, REJECT the null hypothesis. </li></ul>
  5. 5. Make a Decision <ul><li>Based on statistical thresholds: </li></ul><ul><ul><ul><li>/OBS/ < CRIT – Accept Null </li></ul></ul></ul><ul><ul><ul><li>/OBS/ > CRIT – Reject Null </li></ul></ul></ul><ul><ul><ul><li>P-value < Alpha-level = Reject Null </li></ul></ul></ul><ul><ul><ul><li>P-value > Alpha-level = Accept Null </li></ul></ul></ul><ul><li>Form a conclusion </li></ul><ul><li>Make a recommendation </li></ul>
  6. 6. Case Overview <ul><li>Food servers’ tips in restaurants may be influenced by many factors: </li></ul><ul><ul><li>The nature of the restaurant </li></ul></ul><ul><ul><li>Size of the party </li></ul></ul><ul><ul><li>Table location in the restaurant </li></ul></ul><ul><ul><li>Etc. </li></ul></ul><ul><li>To make appropriate assignments for the food servers, restaurant managers need to know what these factors are. </li></ul><ul><li>Must avoid unfair treatment of the food servers, for whom the tips are a major component of pay. </li></ul>
  7. 7. Case Overview (cont.) <ul><li>Based on one food server’s data about all customers over a two and a half month period </li></ul><ul><li>The data was recorded on those days and during times when the food server was routinely assigned to work. </li></ul><ul><li>The following information was recorded: </li></ul><ul><ul><li>The amount of the total bill </li></ul></ul><ul><ul><li>The amount of the tip </li></ul></ul><ul><ul><li>The gender </li></ul></ul><ul><ul><li>Smoker vs. Non </li></ul></ul><ul><ul><li>The day of the week (3=Thu, 4=Fri, 5=Sat, 6=Sun) </li></ul></ul><ul><ul><li>Time of day (day, night) </li></ul></ul><ul><ul><li>Size of the party (1-6) </li></ul></ul><ul><li>Case Question : Based on this data, what are your recommendations to avoid unfair treatment of the food servers? </li></ul>
  8. 8. Summary Measures <ul><li>245 Total Observations </li></ul><ul><li>Average Total Bill: $19.79 </li></ul><ul><li>Mean Tip: $3.00 or 15.2% </li></ul><ul><li>Average Party Size: 2.5 </li></ul><ul><li>Mean Tip by Shift: $2.73 (Day) & $3.10 (Night) </li></ul><ul><ul><li>68 Day & 176 Night Shifts </li></ul></ul><ul><li>Mean Tip of Males: $3.09 </li></ul><ul><li>Mean Tip of Females: $2.83 </li></ul><ul><li>151 Non-Smokers ($2.99) & 93 Smokers ($3.01) </li></ul>
  9. 13. Hypothesis Test 1 <ul><li>Question : Are Saturdays & Sundays the best days for tips? </li></ul><ul><li>Null: Saturday & Sunday ARE the best days for tips. </li></ul><ul><li>Alt: Saturday & Sunday are NOT the best days for tips. </li></ul><ul><li>Hypothesized Value: $3.00 </li></ul><ul><li>Sample Size: 163 </li></ul><ul><ul><li>Only 81 Thursdays & Fridays </li></ul></ul><ul><li>Sample Mean: $3.12 </li></ul><ul><li>One – Tailed Test </li></ul>
  10. 14. Hypothesis Test 1 (cont.) <ul><li>Test Statistic (OBS) = 1.007 </li></ul><ul><li>Critical Measure = 1.645 </li></ul><ul><li>/OBS/ > Crit? = NO </li></ul><ul><li>P-value = 0.157 </li></ul><ul><li>Alpha-level = 0.05 </li></ul><ul><li>P-value < Alpha? = NO </li></ul><ul><li>ACCEPT NULL!!! </li></ul><ul><li>Conclusion : Saturday & Sunday ARE the best days for tips. </li></ul><ul><ul><li>Average tip for Thursday & Friday is $2.76 </li></ul></ul>
  11. 15. Hypothesis Test 2 <ul><li>Question : Do smaller parties tip better than average? </li></ul><ul><li>Null: Smaller parties DO tip better. </li></ul><ul><li>Alt: Smaller parties do NOT tip better. </li></ul><ul><li>Hypothesized Value: $3.00 </li></ul><ul><li>Sample Size: 198 (sizes 1-3) </li></ul><ul><ul><li>Only 46 Large Parties (sizes 4-6) </li></ul></ul><ul><li>Sample Mean: $2.71 </li></ul><ul><li>One – Tailed Test </li></ul>
  12. 16. Hypothesis Test 2 (cont.) <ul><li>Test Statistic (OBS) = (3.442) </li></ul><ul><li>Critical Measure = 1.645 </li></ul><ul><li>/OBS/ > Crit? = YES </li></ul><ul><li>P-value = 0.000 </li></ul><ul><li>Alpha-level = 0.05 </li></ul><ul><li>P-value < Alpha? = YES </li></ul><ul><li>REJECT NULL!!! </li></ul><ul><li>Conclusion : Smaller parties do NOT tip better. </li></ul><ul><ul><li>Large parties average tip is $4.22 </li></ul></ul>
  13. 17. Conclusion <ul><li>Males tip better than Females </li></ul><ul><li>Saturdays & Sundays are the best days for tips. </li></ul><ul><li>Large Parties tip better than smaller parties, although there are many more smaller parties. </li></ul><ul><li>Night Shift usually gets better tips </li></ul>
  14. 18. Recommendation <ul><li>Schedule food servers on an alternating week to week routine based on day and shift: </li></ul><ul><ul><li>Days 3 & 5 (Thursday & Saturday) </li></ul></ul><ul><ul><ul><li>Mean tip $2.88 </li></ul></ul></ul><ul><ul><li>Days 4 & 6 (Friday & Sunday) </li></ul></ul><ul><ul><ul><li>Mean tip $2.99 </li></ul></ul></ul><ul><li>All servers will also alternate Day & Night shifts for equal opportunity. </li></ul>