1. HIMS 650

2. * To learn how to use the Excel program, watch these helpful Youtube.com videos: https://www.youtube.com/watch?v=8L1OVkw2ZQ8 https://www.youtube.com/watch?v=lJqfZw5j2R0 https://www.youtube.com/watch?v=rpCaVZCURZQ https://www.youtube.com/watch?v=sYxiYzx0_yY https://www.youtube.com/watch?v=RIIcRArOCok https://www.youtube.com/watch?v=qZbWJC7mO4o https://www.youtube.com/watch?v=csQrfaAXin0 https://www.youtube.com/watch?v=YU-KmgpG-ew HIMS 650 Homework 12

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4. * Use the file, Chpt 04-1.xls that is posted in the Course Content under Homework – Files Needed * The next slide shows you a screen shot of where the Chpt 04-1.xls file is located in the HIMS 650 classroom HIMS 650 Homework 1 4

5. 5 Screenshot from HIMS 650 Classroom

6. * Select the variable Age and do the following: * Using the =MIN(), =MAX(), and =FREQUENCY() functions, replicate Figure 4.2 * =MIN(), and =MAX() are self explanatory * =FREQUENCY() is an array function HIMS 650 Homework 1 6

7. * From Excel help: “FREQUENCY is entered as an array formula after you select a range of adjacent cells into which you want the returned distribution to appear… * Formulas that return arrays must be entered as array formulas * To enter an array formula (for Mac) press Command + Return * For Windows, press Ctrl+Shift+Return HIMS 650 Homework 17

8. * My data for Age is listed in cells A2:A101 (A colon or “:” means “to” so A2:A101 is read as cells A2 to A101) * My Bin data is listed in cells D2:D7 (I simply copied the Bin numbers from page 106 of your textbook) * To use =FREQUENCY(), I must put both the data array and the Bin array into the formula * Therefore, my formula is typed as =FREQUENCY(A2:A101,D2:D7) into cell E3 (Do NOT press return yet) * Since it is an array function, instead of just using the Return key, I use both the Command and Return keys * Press Command + Return (for Mac) OR Ctl+Shift+Return (for Windows) HIMS 650 Homework 1 8

9. * By clicking on both Command+Return, Excel puts a bracket {} around the formula so that it now looks like the following (in cell E3): * {=FREQUENCY(A2:A103,D3:D8)} * The first time that I use the =FREQUENCY() function, it returns one number, so I need to redo it by…. HIMS 650 Homework 1 9

10. * Highlight the cells E2:E8 by clicking on cell E2 and then hold down the shift key and clicking on cell E8 * With the cells highlighted, click Control + U (for Mac) * Next click Command + Return (for Mac) or Ctrl + Shift + Return (for Windows) * All of the cells, E2:E8 should contain numbers which equal the numbers in Figure 4.2 on page 106 HIMS 650 Homework 1 10

11. * You can learn how to create charts and graphs by watching the Youtube.com videos listed on Slide 2 * Don’t forget to add the correct labels when you create your charts HIMS 650 Homework 1 11

12. * Generate a cumulative frequency for the variable Age as well as percentage and cumulative percentage distributions as shown in Figure 4.13 * Figure 4.13 shows what your answer should look like * Figure 4.14 shows you the formulas to enter into each cell to make your answer correct * Part h should be self explanatory HIMS 650 Homework 112

13. Figure 4.13 HIMS 650 Homework 1 13

14. Figure 4.14 HIMS 650 Homework 1 14

15. * Problem 4.1 3 is similar to problem 4.1 1 * Simply follow the procedure to create a frequency distribution like you did in previous slides, using the data found in the SWC tab (using the IMR – Infant Mortality Rate column data) in the Chpt 04-1.xls spreadsheet (where you previously found the data for Age) * Replicate figure 4.18. Don’t forget to create bins before using the =FREQUENCY() formula. What are your Bin numbers? * Remember that =FREQUENCY() requires both the IMR data and the Bin data HIMS 650 Homework 115

16. * I like using Chart Quick Layouts number 9, so I can easily edit the axes and the Chart title * The next slide shows my reproduction of Figure 4.18 HIMS 650 Homework 116

17. Graph of Reproduced Figure 4.18 HIMS 650 Homework 1 17

18. * By now you should be very familiar with creating frequency data * Generate a frequency distribution of five Bins for under-five mortality (USMR) and produce a column graph for that variable * The only difference for part b is that you create your own Bins. If you need 5 Bins, how would you get the numbers? * Finally, use the textbook to discuss the skewedness of the chart that you just created HIMS 650 Homework 118

19. * Use the variable Sex on the Hospital Charges sheet in Chpt 04- 1.xls and Create a frequency distribution using the pivot table …, using Count of sex in the DATA field. * The textbook teaches you how to build a Pivot table using Excel 2007. * To learn how to use pivot tables in Excel 2013, use this website: https://support.office.com/en-us/article/Create-a-PivotTable- to-analyze-worksheet-data-a9a84538-bfe9-40a9-a8e9- f99134456576 * Here is a website to teach you how to build a pivot table using Excel for Mac 2011 http://www.techonthenet.com/excel/pivottbls/create2011.php HIMS 650 Homework 119

20. * You create a pivot table in this problem, using different data. Replicate Figure 4.34 * For this problem, you need to download Chpt 04-2.xls from the classroom. The next slide shows the location of that data HIMS 650 Homework 1 20

21. Screenshot from HIMS 650 Classroom HIMS 650 Homework 1 21

22. * Use columns b and d for your pivot table under the tab labeled DRG * Since you have already done a pivot table, this one should be easy for you to create * You have now finished all of the required problems for Chapter 4! * Congratulations! Now onto Chapter 5 problems HIMS 650 Homework 1 22

23. HIMS 650 Homework 123

24. * Probability – the book does an excellent job of explaining probability * Terms to know: Simple (or Marginal) Probability, Conditional probability, and Joint Probability * Figure 5.4 on page 152 is a good summary of these 3 concepts HIMS 650 Homework 1 24

25. * You are back to using pivot table capabilities of Excel for part a. It’s a good thing that you practiced them in Chapter 4! (Don’t forget to drag the field name, Shift, to the Column Tables area) * See Figure 5.6 and the paragraph under that figure to do parts b and c * See Figure 5.9 and the paragraph titled, Calculating Joint probability “or” Values… to complete part d * You learn how to do part e on page 159-160, Bayes’ Theorem and Conditional Probabilities * Don’t forget to answer the last question of part e: confirm that reason for arrival and time of arrival are not independent HIMS 650 Homework 1 25

26. Here is the equation that you will use in problem 1. The next picture shows you how to use it Figure 5.6 Figure 5.6 Equation HIMS 650 Homework 126

27. In this picture, n = 5, x = 3, p = 0.5, and 1-p = 1-.5 or.5. The problem gives you n, x, and p. Simply use the information given in the problem in this equation to find the answers to parts a and b. Simple! Figure 5.6 Equation HIMS 650 Homework 1 27

28. This equation is similar to equation 5.6. In the problem, you are given both x and n. The only concept that you need to Understand is factorial. From page 168, “The term “factorial” means to multiply the number to which the factorial refers by Every number less than it in the number sequence. So, for example, 5! Is 5x4x3x2x1 or 120.” Just substitute, use factorial, and Voila! Figure 5.7 HIMS 650 Homework 1 28

29. This problem is easy! You have already done problems 5.1 and 5.2. Simply do them again with the information in problem 5.3, Then multiply the answers together. Voila! Figure 5.8 HIMS 650 Homework 1 29

30. * We now turn out attention to the =BINOMDIST() function in Excel. (Excel has a function that will calculate the preceding equations for you) * From page 169, “The =BINOMDIST() function takes 4 arguments. These are the number of emergency visits…, the number of visits observed…, the probability of an emergency…, and a 0 or 1 to indicate whether the value to be determined is the actual probability or the cumulative probability.” HIMS 650 Homework 130

31. * Read this website to learn more about the Binomial Distribution: http://stattrek.com/probability-distributions/binomial.aspx * From the website, “The binomial probability refers to the probability that a binomial experiment results in exactly X successes.” * From the website, “A cumulative binomial probability refers to the probability that the binomial random variable falls within a specified range (e.g., is greater than or equal to a stated lower limit and less than or equal to a stated upper limit) * Know the difference between a binomial probability and a cumulative binomial probability HIMS 650 Homework 131

32. * Excel’s =BINOMDIST() function: read this website to learn how Excel calculates =BINOMDIST() https://support.microsoft.com/en-us/kb/827459/ * Remember that you needed to learn the difference between binomial probability and cumulative binomial probability? * From the website, “Then cumulative =TRUE, the BINOMDIST(x, n, p, cumulative) function returns the probability of x or fewer successes in n independent Bernoulli trials…When cumulative = FALSE, BINOMDIST returns the probability of exactly x successes.” * Most of the time, cumulative will = 1 in your problems HIMS 650 Homework 1 32

33. * All of the information needed for the =BINOMDIST() function is in problem 5.3 7 * Use =BINOMDIST() to solve problem 5.3 7 * Read the problem carefully. Look for language like “…10 patients or more out of 15…” Will cumulative = 0 or 1 in this case? * This problem should be easy for you to solve since Excel does all of the arithmetic for you HIMS 650 Homework 133

34. * For part a, use =POISSON(x, Average number of arrivals, 0) [=POISSON is compatible with Excel 2007 and =POISSON.DIST is used with Excel 2010 and later] https://www.khanacademy.org/math/probability/random- variables-topic/poisson_process/v/poisson-process-1 * For part b, use the equation 5.9 on page 177 which looks like the following when typed into Excel: = (Average^x*EXP(1)^- (Average))/FACT(x) * For part c, use the numbers generated by part b when you calculate through 9, e.g. calculate POISSON when x = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 etc… * Then use the answers to the POISSON equations to generate a graph * That’s it! HIMS 650 Homework 134

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