(Alexander Klemp)Lab 1-Fall2023.docx

Prof Cary & Werner Fall 2023 Biometrics Lab 1 Name(s): Alexander Klemp You may work individually or collaboratively in a group of 2 people to develop your answers to this lab. If you work collaboratively, clearly explain the contribution of each member to each question . Submit one answer for your group and make sure that the file name identifies the group members. Please, use the appropriate Greek/Latin symbols. If you write or draw any answers by hand, please photograph them and insert the photo in the appropriate position in the lab. Because mathematical formulas and symbols generated in Google Docs might not convert properly when saving as a Microsoft Word document, please submit your work in both Word and pdf formats. Please read the statements below. When you have completed the lab, sign the statement by typing your name in an appropriate blank. By signing this contract, you acknowledge your commitment to the academic honesty policy. Academic Honesty Policy of Beloit College: “In an academic institution, few offenses against the community are as serious as academic dishonesty. Such behavior is a direct attack upon the concept of learning and inquiry and casts doubts upon all measures of achievement. Beloit insists that only those who are committed to principles of honest scholarship may study at the college.” Acts of Academic Dishonesty “Cheating is an act of deception by which a student misrepresents that he/she has mastered information on an academic exercise that he/she has not mastered. For example, intentionally using or attempting to use unauthorized materials, information, or study aids in any academic exercise is considered cheating.” I, Alexander Klemp, hereby acknowledge that the academic work presented in this exam is an honest reflection of my own learning. 1

Prof Cary & Werner Fall 2023 Word identification: Fill in the blank with the term that is defined. (2 points each) 1. Median A measure that describes the middle of a set of measurements. 2. Population All members of a group. 3. Precision The nearness of a measurement to other measures of the same. 4. Variation The sum of the squared deviations from the mean. 5. Parameter The general term for a quantity that describes an aspect of a random sample drawn from a population. 6. Continuous variables A variable with an infinite number of possible values between any two values. 7. Probability The likelihood or relative frequency of an event. 8. Random sample A sample chosen in such a way that every member of the population has an equal and independent chance of being chosen. 9. What is the mathematical formula for sample variance? Please describe each of the terms in the equation. (3 points) 𝑆 2 = 𝑖=1 𝑛 ∑ (𝑥 𝑖 −𝑥 ) 2 𝑥 −1 ● is value of the element 𝑥 𝑖 𝑖 𝑡ℎ ● is sample mean 𝑥 ● n is sample size ● is sample variance 𝑆 2 2

Prof Cary & Werner Fall 2023 d. Generate a cumulative frequency polygon of the data. Add the table and graph here. a. %fat cum freq 4.0-6.0 5 6.1-8.0 32 8.1-10.0 65 10.1-12.0 88 12.1-14.0 93 14.1-16.0 107 16.1-18.0 120 18.1-20.0 122 20.1-22.0 125 22.1-24.0 126 b. c. 4

Prof Cary & Werner Fall 2023 e. Use the data and figures to answer the following questions. Include the mathematical formulas you used to calculate any statistics. ● What is the median % fat content? i. 126/2= 63 ii. Value 63 = 21.2 ● Determine the sample mean, sum of squares, variance, and standard deviation of % fat content. i. mean=average(F2:F127)= 10.97698 ii. Sum of squares= iii. variance= iv. Standard deviation=STDEV.S(F2:F127)=3.94178 ● Determine the coefficient of variation. i. 3.94/10.97 = .35 ● How many observations were greater than 10.5%? i. 58 observations 11. Install the UsingR package in R Studio and bring it in to memory. Load the “five.yr.temperature” dataset. This dataset contains 2,439 observations of the temperature in New York City over the span of five years. Use these data to complete the following tasks in R Studio. You will need to show both the answer to the questions below as well as your work (what call you typed into R to get that answer). The best way to do this is to insert screenshots. (30pts) a. What are the mean, median, variance, and standard deviation of the temps variable? Mean: 55.83649 Median: 56.3 Var: 281.0948 sd: 16.76588 5

Prof Cary & Werner Fall 2023 12. You are given 45 mice ( Mus musculus ) to use in an experiment. The first cage contains 5 white mice, 5 brown mice, and 5 black mice. The second cage contains 3 white mice, 4 brown mice, and 8 black mice. The third cage contains 4 white mice, 7 brown mice, and 4 black mice. a. If one mouse is selected from each cage, what is the probability of selecting 3 brown mice? Please show the formulas that you used to answer this question. (3 points) .33×.267×.46= 4% b. If one mouse is selected from each cage, what is the probability of selecting 1 white mouse and 2 black mice? Please show the formulas that you used to answer this question. (3 points) .33×.20×.267=1.7% .33×.53×.267=4.6% 1.7%×4.6%=>1% 13. When designing experiments, it is often important to “balance” treatments to control for order effects. Suppose that you have 5 possible scents and you want to present 3 of those scents to each rat (scents are presented to each rat one at a time). (6pts) a. Are these arrangements combinations or permutations? Why? These are combinations because the order presented doesn’t matter b.Determine the number of ways (i.e., the different sequences) the 3 selected scents could be arranged. Show your formula and mathematical work. 𝑛! (𝑛−𝑟)!𝑟! c. Using this information, design a study using 300 rats in which you control for order effects. ( Hint : remember that arrangement of scents should be randomly assigned to rats.) Get 300 rats and put ten groups of 30 in 10 different cages and then expose them to the scents randomly. 7

Prof Cary & Werner Fall 2023 14. Students sampled a specified area of the restored oak savannah adjacent to the Science Center and recorded the frequency of each plant/tree in the frequency table below (let’s assume these are the only species present). Use these data to answer the following questions (13pts). Species Frequency White oak ( Quercus alba ) 5 Black-eyed susan ( Rudbeckia hirta ) 38 Purple coneflower ( Echinacea angustifolia ) 57 Prairie coneflower ( Ratibida columnifera ) 31 Common milkweed ( Asclepias syriaca ) 16 a. Determine the relative frequency for each species in the sample (for simplicity, you may add a column to the table above). Species Relative Frequency White oak ( Quercus alba ) 5/147 Black-eyed susan ( Rudbeckia hirta ) 38/147 Purple coneflower ( Echinacea angustifolia ) 57/147 Prairie coneflower ( Ratibida columnifera ) 31/147 Common milkweed ( Asclepias syriaca ) 16/147 b. Use the Shannon’s index to calculate the plant species diversity. 1.4 𝑖=1 5 ∑ 𝑝 𝑖 𝑙𝑛(𝑝 𝑖 ) c. Calculate the Shannon evenness for these data. Please show the formulas and all intermediate steps you used to make your calculations. H/lnS -6.3283 d. From your calculations, determine whether you think this sample has relatively low or high species diversity. Justify you conclusion. It has a low diversity because the shannon's index is low Let’s suppose that Beloit College students have been sampling the Science Center prairie multiple times per year for the past 15 years. From all of these sampling periods, a probability has been determined for the five plant species. Use these probabilities to answer the following questions: Species Probability White oak ( Quercus alba ) 0.02 Black-eyed susan ( Rudbeckia hirta ) 0.24 8