Exploring Probabilities through Bootstrapping Simulation - Prof. Debra Wood, Study notes of Mathematics

Instructions for running simulations using excel to estimate probabilities based on given data sets. The simulations involve modifying worksheets to estimate the probability of certain events, such as the last call arriving before or after a specific time in the phone log example, or the business gross sales being under a certain amount for federal or state assistance programs. The document also discusses the concept of bootstrapping and its relevance to simulations.

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Pre 2010

Uploaded on 08/31/2009

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WS 15 – Random Sample Name:
Bootstrapping - Simulation #
This simulation is written for you, run the simulation and modify the file for different information
1. This simulation has been created for you. Read the text and understand the excel file along with
the functions covered in class. Slides 125-134. The text explains this problem and step by step on what
to do. You must understand the file so you can then modifying it to find new results. Hit F9 a few times
to see what is going on. I want you to investigate this excel file. Once you understand the file and what
is in each cell you will know how to answer the questions below.
For some questions you are going to modify this file. Suggestion: create a new worksheet before
making the changes, that are required to the existing file, modify this new worksheet. Make a new
worksheet for each modification. Save your work. This is a strategy you should always do when given a
file from our text.
This is the scenario from the text:
State how you modified the worksheet (if you did) to get the desire results, then
state the results.
A. (i) Use Phone Log.xls to estimate the probability that the last call in a run of 50 calls, starting at
9:00 a.m., will arrive before 10:00am. (No changes in the worksheet)
(ii) Show the probability of 5 different simulations.
(iii) What is the average probability of these 5 simulations?
(iv) Show the probability of 10 new different simulations
(v) What is the average probability of these 10 simulations?
(vi) What is the average probability of all 15 simulations?
(vii) How many total runs when you do 15 simulations?
B. Exercise 17: (i) Use Phone Log.xls to estimate the probability that the last call in a run of 50
calls, starting at 9:00 a.m., will arrive after 10:20 a.m. (ii) Show the probability of 5 different
simulations. (iii) What is the average probability of these 5 simulations.
Your work needs to include what cell(s) you changed and what is now written in the cell(s).
C. Exercise 18 (i) Use Phone Log.xls to estimate the probability that a run of 30 calls, starting at
9:00 a.m., will arrive before 9:30 a.m.
Your work needs to include what cell(s) you changed and what is now written in the cell(s).
Random Sample The operator of a phone switchboard at a large company takes a break
after every 50 calls that he handles. To plan for a backup operator, the office manager would
like to have information on the length of time that it might take for a set of 50 calls to arrive
at the switchboard. Specifically, you would like to know the probability that, starting at
9:00am, a run of 50 calls will arrive before 10:00am.
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Bootstrapping - Simulation # This simulation is written for you, run the simulation and modify the file for different information

1. This simulation has been created for you. Read the text and understand the excel file along with

the functions covered in class. Slides 125-134. The text explains this problem and step by step on what to do. You must understand the file so you can then modifying it to find new results. Hit F9 a few times to see what is going on. I want you to investigate this excel file. Once you understand the file and what is in each cell you will know how to answer the questions below. For some questions you are going to modify this file. Suggestion: create a new worksheet before making the changes, that are required to the existing file, modify this new worksheet. Make a new worksheet for each modification. Save your work. This is a strategy you should always do when given a file from our text. This is the scenario from the text: State how you modified the worksheet (if you did) to get the desire results, then state the results. A. (i) Use Phone Log.xls to estimate the probability that the last call in a run of 50 calls, starting at 9:00 a.m., will arrive before 10:00am. ( No changes in the worksheet ) (ii) Show the probability of 5 different simulations. (iii) What is the average probability of these 5 simulations? (iv) Show the probability of 10 new different simulations (v) What is the average probability of these 10 simulations? (vi) What is the average probability of all 15 simulations? (vii) How many total runs when you do 15 simulations? B. Exercise 17: (i) Use Phone Log.xls to estimate the probability that the last call in a run of 50 calls, starting at 9:00 a.m., will arrive after 10:20 a.m. (ii) Show the probability of 5 different simulations. (iii) What is the average probability of these 5 simulations. Your work needs to include what cell(s) you changed and what is now written in the cell(s). C. Exercise 18 (i) Use Phone Log.xls to estimate the probability that a run of 30 calls , starting at 9:00 a.m., will arrive before 9:30 a.m. Your work needs to include what cell(s) you changed and what is now written in the cell(s). Random Sample The operator of a phone switchboard at a large company takes a break after every 50 calls that he handles. To plan for a backup operator, the office manager would like to have information on the length of time that it might take for a set of 50 calls to arrive at the switchboard. Specifically, you would like to know the probability that, starting at 9:00am, a run of 50 calls will arrive before 10:00am.

Bootstrapping - Simulation # Run a simulation using actual data (Bootstrapping) – started one on Monday

2. Random Sample slide 135 Example 20 A. The business whose daily sales data are shown in the Excel file Daily Sales.xls will be eligible to apply for a federal assistance program if its gross sales on 8 randomly selected business days are all under $7,000. (i) Use the functions RANDBETWEEN, VLOOKUP , and MAX in the sheet Raw Data to simulate 3,000 sets of eight-day gross sales records. (similar to class except you will use all 1000 days) ( State what you type in the cell(s) to set up this simulation ) (ii) Use CONDITIONAL FORMATTING (slide 147-148) and highlight (either yellow or red) all those cells that are under $7000. (Print 3 sets of the 8 randomly business days) I know when printed the highlighted area will be gray if you print with just black (iii) Use the COUNTIF function to estimate the probability that the business will be eligible for the federal program. (Show what you typed in the cell to get this value) (give your probability as a percent with 1 decimal place) (iv) Using F9 write the probability of 5 simulations of 3,000 runs – what is this average? (v) Is 3000 simulations enough to get a reasonable probability? Explain (vi) Why is this simulation called bootstrapping? Answer the questions and show 3 lines of your simulation and describe what is in each cell Show the results of the probability of the 5 simulations and then state the average of them B. Random Sample Exercise 21 The business, whose daily sales data are shown in the Excel file Daily Sales.xls , will be eligible to apply for a federal assistance program if its gross sales on 8 randomly selected business days are all under $8,000. Use the COUNTIF function to estimate the probability that the business will be eligible for the federal program. (give your probability as a percent with 1 decimal place) Simulation is 3000 runs Make a copy of previous work and modify the cells to get this new result Solution Explain what you typed in cell(s) you changed from part A. Show the probability results of 5 simulations and take that average. C. Consider the business situation in Exercise 20(part A). Eligibility for a state assistance program requires that the average daily gross sales for 8 randomly selected business days must be under $6,000. Simulate 3,000 sets of eight-day gross sales records and use these to estimate the probability that the business will be eligible for the state program (give your probability as a percent with 1 decimal place) Solution Explain what you typed in cell(s) you changed from part A. Show the probability results of 5 simulations and take that average.

Bootstrapping - Simulation # g. Copy the worksheet you just created to a new worksheet. Now using the list below of 16 values and using the simulation you just created (the simulation 5000 runs) predict the average. Run your simulation 5 times recorded the average of each simulation. Now take the average of the 5 simulations. Find the actual average of these 16 values. Compare your simulation average of 1 run, of the 5 runs to the actual value. By how many decimal places? Make a duplicate copy of your previous worksheet and change the values in your table then run the simulation. A B 1 3 2 3 3 3 4 3 5 7 6 7 7 7 8 7 9 7 10 7 11 7 12 7 13 10 14 10 15 10 16 20