Class Note for MATH 115A with Professor Wood at UA 2
Class Note for MATH 115A with Professor Wood at UA 2
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Date Created: 02/06/15
WS 15 7 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 le along with the functions covered in class Slides 125134 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 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 900am a run of 50 calls will arrive before 1000am State how you modified the worksheet if you did to get the desire results then state the results A i Use Phone L0gxls to estimate the probability that the last call in a run of 50 calls starting at 900 am will arrive before 1000am 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 L0gxls to estimate the probability that the last call in a run of 50 calls starting at 900 am will arrive after 1020 am ii Show the probability of 5 different simulations iii What is the average probability of these 5 simulations Your work needs to include what cells you changed and what is now written in the cells C Exercise 18 i Use Phone L0gxls to estimate the probability that a run of 30 calls starting at 900 am will arrive before 930 am Your work needs to include what cells you changed and what is now written in the cells WS 15 7 Random Sample Name Bootstrapping Simulation Run a simulation using actual data Bootstrapping 7 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 Salesxls will be eligible to apply for a federal assistance program if its gross sales on 8 randomly selected business days are all under 7000 i Use the functions RANDBETWEEN VLOOKUP and MAX in the sheet Raw Data to simulate 3000 sets of eight day gross sales records similar to class except you will use all 1000 days State what you type in the cells to set up this simulation ii Use CONDITIONAL F ORMATTING 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 3000 runs 7 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 Salesxls will be eligible to apply for a federal assistance program if its gross sales on 8 randomly selected business days are all under 8000 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 cells 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 6000 Simulate 3000 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 cells you changed from part A Show the probability results of 5 simulations and take that average WS 15 7 Random Sample Name Bootstrapping Simulation The expected value is the average which is also called the mean The average or mean from a sample is called a sample mean denoted by u 5 or 9 3 This exercise is to see why a simulation can be used in making predictions How many runs are needed in a simulation in order to think the prediction is close to the actual value In this example we are going to see how many runs are needed to get close to the actual averagemeanexpected value For many sets of data we don t know the actual average The only average we can calculate is the average from the sample This is to help understand why many runs are needed in a simulation How do we know how many runs are needed You will be creating a simulation from scratch a Open an excel file and create a table with the following 16 entries A B DOONOUIJRWNH l tl tl tl tl tl t Lthth O INQMMJAJKJkkWWNNNH i 0 Scenario is there are 16 pieces of paper with the values that are found in column B If one picks 5 of these pieces of paper at random with replacement what is the expected value averagemean b Using excel find the average value of these 16 numbers average to 4 decimal places 0 Now create a run where 5 cards are randomly drawn you will use randbetween and vlookup add another column that contains the average of these 5 values 5 decimal places Show this run with the titles and values Hit F9 a few times at least 6 times does this one random pick of 5 cards uctuate Record the high and the low average Are you always close to the true average d Now create a simulation with 100 runs Add a column that finds the average of these 100 runs State the average of the 100 runs to 5 decimal places Hit F9 and record the 100 run average 6 times Does the average of the 100 runs uctuate Are you close to the true average by how many place values 6 Now expand the simulation with 1000 runs Does the average of these 1000 runs uctuate Hit F9 at least 6 times Is it close to the actual average By how many place values f Now extend your file to make a simulation with 5000 runs Does the average of these 5000 runs uctuate Hit F9 Are they close to the actual average By how many place values or within how many units nearest hundredth within nearest 5 thousandth WS 15 7 Random Sample Name 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 i 0 D O
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