Biostatistics Homework #4: Key Questions for Spring 2024

381.SP24 Homework #4 Questions 381.SP24 Homework #4 Questions 381.SP24 Homework #4 Questions SPH-Q 381.SP24 Introduction to Biostatistics—Spring 2024 Dr. Dave Fluharty Homework #4 6 Points 12 Questions ½ Point Each DUE March 8, 2024 Not considered late until March 20,2024 No late assignments accepted except in exceptional circumstances. You may use your book, notes, videos, internet, or other resources. You may discuss the questions with other students, HOWEVER, THE ASSIGNMENT YOU SUBMITT MUST BE DONE INDIVIDUALLY. For example, you might meet with a study group to discuss what questions mean and how they might be approached (including hints for JMP), but then separate and do the problems yourself. Contact Dr. Dave if this is unclear. We will review the homework questions in the first class after the homework is uploaded. Students may also ask Dr. Dave questions about this homework during Drop-In Office Hours or individual meetings. INSTRUCTIONS: 1. BE SURE TO READ THE ENTIRE QUESTION BEFORE ANSWERING IT (in the past students have lost points on this). 2. If a question involves calculations, write out your calculations. Do not just write down the answer unless it is just looking up a value. First write the formula you used and then show the calculations. 3. Submit the assignment in Microsoft Word or PDF format. a. Do not submit in other formats which may not be readable for grading. b. Please put your answers in a different color than the questions (this makes grading much easier). c. Be sure the answers you upload are complete. You are responsible for ensuring you uploaded the entire assignment. 4. Please read the questions carefully. In the past students have lost points for not answering the question that asked or not answering all of the question. If you have any questions—particularly if you have difficulty working with JMP--please contact Dr. Dave!! PURPOSE OF THIS HOMEWORK: Ensure you understand some concepts of probability and can use tables and jmp to calculate binomial and Poisson probabilities. Page 1 of 11

381.SP24 Homework #4 Questions 381.SP24 Homework #4 Questions 381.SP24 Homework #4 Questions GENERAL HINTS: Formulas are provided in some of the questions. JMP HINTS: 1. jmp’s© Distribution Calculator is found in the with the following menu path: >Help >Sample Index >Calculators (in “Teaching Resources” box near the bottom of the menu) >Distribution Calculator 2. When you are asked to calculate a probability using jmp©: a. Write the probability in your homework. This is found at the bottom of the “Calculations” box. 3. When you do the calculation in jmp©, you need to select the correct “Probability Option.” Once you do check the graph of the probability distribution. If you have any questions, please ask Dr. Dave. QUESTIONS: Page 2 of 11

381.SP24 Homework #4 Questions 381.SP24 Homework #4 Questions 381.SP24 Homework #4 Questions 1. True or False: The graph below fairly represents the probability of the outcomes of the number of times a 1 is thrown in an infinite number of experiments? 2. What are the two basic types of distributions? Hint: One is calculated from data and the other is based on a mathematical formula. 3. What are the two types of data for which we have studied theoretical distributions? Hint: One concerns counts. 4. What are the three ways of displaying a probability distribution. Hint: One is a table (for discrete data). 5. True or False: Theoretical distribution have parameters and empirical distribution have statistics. 6. True or False: We often use statistics calculated from data to estimate the parameters of a distribution, that distribution being consistent with the data sampled from a population or generated by a process that generated the data. 7. Using jmp©, determine the following probabilities. Hint: This should be the same answer as 8a. Page 3 of 11

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381.SP24 Homework #4 Questions 381.SP24 Homework #4 Questions 381.SP24 Homework #4 Questions a. Binomial n = 7 p = 0.25 x < = 5 (less than or equal to 5) i. Probability = ______________ ii. Cut and paste your jmp© output below. b. Binomial Hint: This should be the same answer as 8b. n = 7 p = 0.25 x = 5 (equal to 5) i. Probability = ______________ ii. Cut and paste your jmp© output below. 8. Question on the Binomial Page 4 of 11

381.SP24 Homework #4 Questions 381.SP24 Homework #4 Questions 381.SP24 Homework #4 Questions a. On the Binomial table below, circle appropriate probability(ies) and write your answer here ________________________________ Hint: if there is more than one probability, write them all and add them up. NOTE: If you cannot circle the probability(ies) in the table, write the column and n(s), the intersection of which gives these probabilities. n = 7 p = 0.25 x <= 5 (less than or equal to 5) Page 5 of 11

381.SP24 Homework #4 Questions 381.SP24 Homework #4 Questions 381.SP24 Homework #4 Questions b. On the Binomial table below, circle the appropriate probability(ies) and write your answer here ________________________________ Hint: if there is more than one probability, write them all and add them up. NOTE: If you cannot circle the probability(ies) in the table, write the column and n(s), the intersection of which gives these probabilities. n = 7 p = 0.25 x = 5 (equal to 5) Page 6 of 11

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381.SP24 Homework #4 Questions 381.SP24 Homework #4 Questions 381.SP24 Homework #4 Questions 9. Assume ambulances arrive at an emergency room at the rate of µ= 3 per hour (reminder μ = λt). a) In the table below, circle the probabilitie s representing 4 or more ambulances arrive in a given hour (if you cannot circle the probabilities, write the µ of the column and the k in which the probabilities you would add up start), and b) write your answer here: __________________________(you do not have to show the calculation) Page 7 of 11

381.SP24 Homework #4 Questions 381.SP24 Homework #4 Questions 381.SP24 Homework #4 Questions 10. Using jmp© , Assume ambulances arrive at an emergency room at the rate of µ = 3 per hour , what is the probability 4 or more ambulances will arrive in an hour. Hint: µ =λt is called “Mean” in the Distribution Calculator. Hint: you should get the same answer as in #9, a) Probability = _________________ b) Cut and past the jmp© output below. 11. Using the formula below, calculate the binomial probability when n =7 p = .25 x = 5 Hint #1: You answer should be the same as 6b and 7b. Hint #2: You can look at Art of Stat web apps Web Apps (artofstat.com) > Distributions: Explore Shapes & Find Probabilities > Binomial Distribution >Formulas and Probabilities tab Page 8 of 11

381.SP24 Homework #4 Questions 381.SP24 Homework #4 Questions 381.SP24 Homework #4 Questions 12. This is a question on Bayes theorem. You are a member of a team which is investigating health care disparities. Your job is to interview people who have been chosen at random to be interviewed. Using the data below cut and pasted below, answer the following questions: a. If you are about the interview a person, and you do not know if they have health insurance, what is the probability that they are Hispanic or Latino? This can be answered by looking at the information given in the table below. b. Explain your answer in “a”. c. If you are told they do NOT have health insurance, what is your estimate that the person you are about to interview is Hispanic or Latino. Hint: Use Bayes Theorem and for your own benefit write out the meaning of the following in words, P(B | A) see “Census Bureau Releases . . .” P(B | A) is the Probability of NOT having health insurance if a person is Hispanic or Latino P(A) see Race and Hispanic Origin Table P(B) see article “New HHS Report . . .” P(A | B) is obtained with the formula for Bayes’ theorem below: d. What, in your own words, is an explanation of why your answers to a and c are different. DATA are in the articles below: According to the US Census Bureau Quick Facts U.S. Census Bureau QuickFacts: United States : Uninsurance Rates New HHS Report Shows National Uninsured Rate Reached All-Time Low in 2022 | HHS.gov Page 9 of 11

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381.SP24 Homework #4 Questions 381.SP24 Homework #4 Questions 381.SP24 Homework #4 Questions Page 10 of 11

381.SP24 Homework #4 Questions 381.SP24 Homework #4 Questions 381.SP24 Homework #4 Questions Census Bureau Releases New Report on Health Insurance by Race and Hispanic Origin Page 11 of 11

SPH-Q 381.SP24 Homework 4 QUESTIONS FEB 2024

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