BME 335 - Homework 1 - Solutions

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University of Texas *

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335

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Mechanical Engineering

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Dec 6, 2023

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BME 335 – HOMEWORK 1 - SOLUTIONS Due Sept 2, 2022 at 11:59 pm on Gradescope Homework should be completed individually. Homework is graded out of 60 pts. There is a total of 120 pts possible in this homework set. You may do as many problems as you want to earn as many points as possible, with a maximum score of 60 points. For example, if you earn 50 pts, your score will be 50/60. If you earn 70 pts, your score will be 60/60. If you earn 120 pts, your score will be 60/60. It is to your advantage to try as many problems as possible to maximize your score. NOTE: All problem narratives are fictitious unless otherwise indicated. 1. Identify if the following variables are numerical or categorical. If the variable is numerical, state whether the variable is discrete or continuous. If categorical, state whether the variable is ordinal or nominal (has no natural order). [8 pts total] 1.1. Number of chemotherapy treatments in a year [1 pt] Numerical, discrete 1.2. Cell membrane surface area [1 pt] Numerical, continuous 1.3. Birth weight [1 pt] Numerical, continuous 1.4. Self-identified gender [1 pt] Categorical, nominal 1.5. Blood glucose level [1 pt] Numerical, continuous 1.6. Proportion of CD8+ T cells to CD4+ T cells [1 pt] Numerical, continuous 1.7. Number of Parkinson’s patients in major US cities [1 pt] Numerical, discrete 1.8. Average rate of a neuron sending action potentials [1 pt] Numerical, continuous 2. A medical researcher Dr. Kiara Richardson wants to know how well Drug DiaBeatIt works to prolong lives of patients after diagnosis with Type I diabetes. She decided she needs 50 patients for conduct a study. Dr. Richardson already has 50 patients she has been treating for this disease over the past decade. She decides to base the study on these patients because she already has access to their records and an ongoing relationship that will make them more likely to participate fully in the trial. [7 pts total] 2.1. What is the technical name for this type of sample? [2 pts] Sample of convenience 2.2. Which criterion of random sampling is most likely to be violated by the problems you identified in part (a): equal chance of being selected or the independence of the selection of individuals? [2 pts] Equal chance of being selected – patients that Dr. Richardson is treating have a much higher chance than other Type I diabetes patients in being included in this study. 2.3. Which attribute of the estimated proportion of patients regularly measuring their blood glucose levels is most affected by the problem you identified in (a): accuracy or precision? Why? [3 pts] The estimate might be biased because it is not a random sample, and bias relates to the accuracy of the estimate. 3. In each of the following examples, indicate which variable is the explanatory variable and which is the response variable. [9 pts total] 3.1. Researchers Moana and Merida randomly divide a sample of Alzheimer’s patients into two groups. Patients in the first group were assigned to receive a new drug, RMember, whereas Intuition and Comprehension [30 pts]

patients in the other group receive standard treatment without the new drug. Moana and Merida compared the beta-amyloid plaque levels in the two groups. [3 pts] Drug treatment: explanatory Beta-amyloid plaque level: response 3.2. Kristoff tested whether the frequency of Phenibut use differs between people suffering from depression and those without depression. He measured drug use in a group of depression patients and compared it with that in a similar-sized group of randomly chosen people. [3 pts] Depression condition: explanatory Phenibut drug use: response 3.3. The anticoagulant warfarin is often used as a pesticide against house mice, Mus musculus . Some populations of the house mouse have acquired a mutation in the vkorc1 gene from hybridizing with the Mickey mouse, Mickey mouseus . In Mickey mice, this gene confers resistance to warfarin. In a study, researchers collect a sample of house mice to determine whether the presence of the vkorc1 mutation is associated with warfarin resistance in house mice as well. They feed warfarin to all the mice in a sample and compare survival between individual subjects possessing the mutation and those not possessing the mutation. [3 pts] Explanatory: mutation status (i.e. mutation vs no mutation) Response: survival 4. Dr. Ricardo Garcia carried out a study in women to determine whether the psychological experience of having an abortion differ from those experienced by women who have lost their fetuses by other causes at the same stage of pregnancy. [6 pts total] 4.1. What is the population of interest in this study? [2 pts] Women who have experienced fetus loss 4.2. What is the explanatory variable and what is the response variable? [2 pts] Explanatory: Reason for fetus loss Response: psychological consequences 4.3. Is this an experimental study or an observational study? Explain. [2 pts] Observational, since Dr. Garcia does not assign treatments (i.e. reason for feus loss) to the women in the samples 5. Average follicle diameter may be measured in women from an ultrasound as a fertility measure. Consider the below measurements (in meters) obtained from a random sample of 26 – 35-year-old women on Day 10 of their menstrual cycle and answer the following questions. [10 pts total] 0.066 0.097 0.080 0.078 0.048 0.090 0.055 0.066 0.078 0.066 0.046 0.081 0.067 0.075 0.048 0.047 0.064 0.041 0.045 0.039 0.065 0.079 0.070 0.066 0.059 0.172 0.056 0.079 0.096 0.077 0.069 0.037 0.075 0.066 0.064 R Application [30 pts]

5.1. In R, create a graph depicting the frequency distribution of the 35 follicle diameter measurements. (Hint: set the number of breaks so that you have 35 bins, that way you’ll see the distribution of the diameters without different diameters being pooled together.) [3 pts] 5.2. Describe the shape of the frequency distribution. What are the main features? [2 pts] The majority of measurements appear to be fairly symmetric about a mode around 0.06 – 0.07 m. However, there is one extreme measurement at 0.172. 5.3. What term would be used to describe the largest measurement in the frequency distribution? [1 pt] Outlier 5.4. In R, create another graph depicting the frequency distribution of the follicle diameter measurements with only 5 bins (Hint: set the appropriate number of breaks to do this). [3 pts]

5.5. What is the mode range of average follicle diameter measurements as depicted in the graph in part (d)? [1 pt] This answer will vary depending on how the student has defined their five bins in 5d. In our plot above, the mode range falls in the bin 0.06 – 0.08 m. 6. A study wants to examine how birth month of babies born during the pandemic may influence diagnosis and treatment of respiratory disease. Below is a table of the fraction of babies aged 6 weeks – 12 months that were diagnosed with a respiratory illness in the first year of life, with the data divided by the month of their birthday. Using the data, answer the following questions. [10 pts total] January 0.13 February 0.14 March 0.12 April 0.10 May 0.09 June 0.10 July 0.07 August 0.06 September 0.07 October 0.09 November 0.08 December 0.11 6.1. In R, create a graph depicting the fraction of babies with respiratory illness by birth month in calendar year order. [3 pts] A bar graph is the best choice for showing data from a single categorical variable (birth month). Since line graphs are also used to show trends over time, a line graph is also an appropriate choice. 6.2. Is there likely an association between birth month and babies with respiratory illness? Explain your reasoning. [3 pts] If there was no association, we would expect the bars to be around equal height year-round. However, it appears that there the fraction of babies with winter birthdays diagnosed with

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