PubHlth Introductory Biostatistics Fall 2012 Examination II Choice A Unit 2 (Introduction to Probability) Due Monday October 8, 2012

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1 PubHlth 540 Fall 2012 Exam II Choice A Page 1 of 9 PubHlth Introductory Biostatistics Fall 2012 Examination II Choice A Unit 2 (Introduction to Probability) Due Monday October 8, 2012 This is Choice A of Two Choices: The exam 2 requirement for this course has two choices. You must choose one of them. Choice A Unit 2 Test (Introduction to Probability) Choice B Unit 3 Test (Populations and Samples) Instructions and Checklist: 1. Start each problem on a new page. 2. Write your name on every page. 3. Make a photo-copy of your exam for safekeeping prior to submission 4. Complete the signature page How to submit your exam: Worcester In-Class Section You may submit your exam in EITHER of 2 ways: 1. Bring your completed exam to class on Monday October 8, 2012, being sure that you have made a copy for safe keeping; OR 2. Mail your completed exam to me with post mark October 8, 2012 to my address below. ONLINE Section You may submit your exam in EITHER of 2 ways: 1. Upload your completed exam to the ASSIGNMENT tab no later than 11:59 pm on Monday October 8, This must be a single pdf and be named using the convention lastname_exam2a.pdf. 2. Mail your completed exam to me with post mark October 8, 2012 to my address below. Address and telephone number for mailing Carol Bigelow School of Public Health/402 Arnold House University of Massachusetts/Amherst 715 North Pleasant Street Amherst, MA Tel

2 PubHlth 540 Fall 2012 Exam II Choice A Page 2 of 9 PubHlth Introductory Biostatistics Fall 2012 Examination II Choice A Unit 2 (Introduction to Probability) DUE: 11:59 PM Monday October 8, 2012 Signature This is to confirm that in completing this exam, I worked independently and did not consult with anyone. Signature: Printed Name: Date:

3 PubHlth 540 Fall 2012 Exam II Choice A Page 3 of 9 1. (10 points total) A local arts and crafts store has found, after many years of experience, 20% of people who enter the store actually buy something. Suppose 3 people enter the store. 1a. (5 points). How many possible outcomes are possible for the sale or non-sale of items to the three potential customers? Hint: In developing your answer, you are actually specifying the sample space for the outcome of sales and non-sales to the three potential customers. 1b. (5 points). What is the probability of at least one sale?

4 PubHlth 540 Fall 2012 Exam II Choice A Page 4 of 9 2. (10 points total) Either allele A or a may occur at a particular genetic locus. An offspring receives one allele from the father and one allele from the mother and these are mutually independent. Suppose one parent possesses alleles A and a and the other parent possesses alleles a and a 2a. (4 points) By hand, calculate the probability of an offspring receiving an A and an a. Show your work. 2b. (3 points) By hand, calculate the probability of an offspring receiving two a alleles. Show your work. 2c. (3 points) By hand, calculate the probability of an offspring receiving two A alleles. Show your work.

5 PubHlth 540 Fall 2012 Exam II Choice A Page 5 of 9 3. (10 points total) Consider the following cross-tabulation of 100 individuals by their smoking status and systolic blood pressure. Shown are counts of individuals. For example, the entry 10 in the first row says that there are 10 non-smokers in this sample with systolic blood pressure between 90 and 109 mm Hg. Systolic blood pressure, mm Hg Non-Smokers Smokers Consider this distribution as a population and, as such, a universe of possibilities from which simple probabilities can be computed. Define two events A and B as follows: A = smoker B = systolic blood pressure of 170 or greater. 3a. (2 points) Find Probability [ A ] 3b. (2 points) Find Probability [ B]. 3c. (6 points) Are A and B independent? Explain.

6 PubHlth 540 Fall 2012 Exam II Choice A Page 6 of 9 4. (20 points total) 4a. (10 points) Perhaps you ve heard the saying if you observe for long enough, a monkey will eventually write a Shakespeare play just by chance. What fun! Consider the setting of putting a typewriter in the hands of a monkey. Assume the typewriter has 50 keys and the monkey types key after key at random. What is the probability that the first seven keys that the monkey types is the seven character title macbeth? 4b. (10 points) Consider a jury trial setting in which the probability that a defendant is convicted, given he or she is actually guilty, is 0.95 and that the probability that a defendant is acquitted, given that he or she is actually innocent is Suppose further that 90% of all defendants are actually guilty. If it is known only that a defendant is convicted, what is the probability that he or she is actually innocent?

7 PubHlth 540 Fall 2012 Exam II Choice A Page 7 of 9 5. (20 points total) Consider the following data on a new screening test for diabetes Diabetes NO diabetes Total Test Test a. (8 points) Using the information in the table, compute the following: 2 points. Sensitivity =, 2 points Specificity = 2 points Predictive value positive = 2 points Predictive value negative = 5b. (8 points) Using the values of sensitivity and specificity from part a and not using your values of predictive value positive from part a, use your understanding of Bayes rule to complete the following table Prevalence Diabetes Predictive Value + Test 5c. (4 points) 2 points. True or False. The sensitivity of a diagnostic test is independent of the probability of disease 2 points True or False. The predictive value of a diagnostic test is independent of the probability of disease.

8 PubHlth 540 Fall 2012 Exam II Choice A Page 8 of 9 6. (10 points total) The following are data from a case-control study that investigated the relationship between helmet use and facial injury following a bicycle accident. Facial Injury Helmet Worn Yes No No Yes a. (2 points) Is this study prospective or retrospective?. 6b. (2 points) What are the odds of a facial injury among persons who did not wear a helmet? 6c. (2 points) What are the relative odds (odds ratio) of facial injury for persons who did not wear a helmet compared to those who did wear a helmet? 6d. (2 points) Is the calculation of the relative risk meaningful in this setting? Explain. 6e. (2 points) Considering your answers to parts a through d, in your opinion, does wearing a helmet reduce the risk of sustaining a facial injury in a bicycle accident? Explain.

9 PubHlth 540 Fall 2012 Exam II Choice A Page 9 of 9 7. (20 points total) The following are hypothetical data from a study of the relationship between cigarette smoking and the risk of low birth weight. Suppose preliminary analyses included the classification of infants into categories according to the number of cigarettes smoked per day by the mother. In particular, suppose the probabilities of the different smoking levels are the following: Cigarettes per day Probability Zero > Total Next, suppose the following conditional probabilities are known. Condition: Mother smokes Conditional Probability of low birth weight infant Zero cigarettes/day > a. (10 points) Calculate the probability of a low birth weight infant. 7b. (10 points) Are the events >20 cigarettes per day and low birth weight infant independent? Explain your reasoning using the rules of probability developed in class.