1015SCG_MathAssignment_T32023

1015SCG Quantitative Reasoning Maths and inference assignment Maths and Inference Assignment 1015SCG Quantitative Reasoning Trimester 3 2023 Weight: 30% Due date: By Friday 22 nd December 2023 (End of week 7) Name: Student number: Third-to-last digit of student number: Use this to determine which data set to use for Question 1. eg digit is 3, use bac3.csv; digit is 0, use bac0.csv. Write this at the top of your answer to Question 1. Second-to-last digit of student number: Use this to determine which data set to use for Question 2. eg digit is 5, use life5.csv, digit is 0, use life0.csv Write this at the top of your answer to Question 2. Last digit of student number: Use this to determine which data set to use for Question 3. eg digit is 7, use workshop7.csv, digit is 0, use workshop0.csv Write this at the top of your answer to Question 3. Instructions:  Please fill out the above information and enter your answers in this Word document .  If your submission is not in the format provided in this Word document, it will not be graded.  Please upload your final assignment as PDF to the submission point on the course site.  Use the correct csv file, if you use a different file, there will be mark penalty.  For each of the questions show your working – explain how the calculations are done, what software and functions are used, show appropriate screenshots from the software.  Make sure all the plots have titles or captions, axes labels with units and a legend if applicable. The scatter plots should be used for discrete data, lines should be used for fits.  Pay attention to significant figures, especially when quoting the values with errors.  The assignment is out of 100 marks. Marks for each question are given with the question in square braces [ ] .  If you have any questions, please ask your demonstrators during the workshops or post your questions (but not answers or solutions) in the course Teams channel. Page 1 of 8 Your name here sxxxxxxx X X X

1015SCG Quantitative Reasoning Maths and inference assignment Question 1 [40 marks] A lab has 10 different bacterial samples, but they all got mislabelled. The growth of the bacteria in specific conditions is given by an exponential function N ( t ) = N 0 e kt , where N 0 is the initial number of bacteria (for the time t = 0 ¿ , N ( t ) is the number of bacteria after time t (measured in days), and k is the growth constant. Values of the growth factor k are different for each type of bacteria and are given in the table. Bacteria type Growth factor k (1/days) Dangerous level C (number of bacteria/cm 3 ) A 0.11 200 B 0.12 310 C 0.13 500 D 0.14 720 E 0.15 550 F 0.16 1020 G 0.17 1300 H 0.18 1560 I 0.19 2000 J 0.20 2500 You are given a random sample in the Petri dish with initially 100 organisms living in a jelly, and you are asked to determine which type of the bacteria it is. You decide to grow the sample, measuring the number of bacteria in your sample every day. Use the file bacx.csv, where x is third-to-last digit of your student number. a) Plot the number of bacteria as a function of time. [5 marks] b) We want to use regression on this data to find the values characterising the sample growth, but to do it we need linear data. What can you plot on the y axis instead the number of the organisms, so the plot becomes linear? Explain and show appropriate equations. [5 marks] Page 2 of 8 Enter your answer here, expand the text box as needed. Enter your answer here, expand the text box as needed.xx

1015SCG Quantitative Reasoning Maths and inference assignment g) In the table, you can find the dangerous level C of each of the bacteria populations in units of the number of bacteria per volume. The volume refers to the volume of the jelly in which the bacteria are growing. The Petri dish has d = 10 cm diameter, and the jelly is h = 5 mm thick. After how many days will the number of bacteria in your sample exceed the dangerous level? [8 marks] Page 4 of 8 Enter your answer here, expand the text box as needed.

1015SCG Quantitative Reasoning Maths and inference assignment Question 2 [30 marks] A research study was conducted to examine the differences between older and younger adults on perceived life satisfaction. Several older adults and several younger adults were given a life satisfaction test. Scores on the test range from 0 to 60, with high scores indicative of high life satisfaction, low scores indicative of low life satisfaction. The data are in the lifex.csv file, where x is the second-to-last digit of your student number. a) Find the best estimates and the standard errors for the life satisfaction score for the old and young adults. [8 marks] b) Plot the data for the old and young adults, where on the y axis is the life satisfaction score and the x axis is a person number. Add a line showing the average to both plots. What can you say about the data in each plot? How do two plots compare? Refer to the values from the previous part. [6 marks] c) Can you say with 95% confidence interval that the life satisfaction scores are the same between these two groups? Show the calculations; explain how you compared the two groups. [8 marks] Page 5 of 8 Enter your answer here, expand the text box as needed. Enter your answer here, expand the text box as needed. Enter your answer here, expand the text box as needed.

1015SCG Quantitative Reasoning Maths and inference assignment Question 3 [30 marks] The data in the workshopx.csv file, where x is the last digit of your student number, gives the workshop attendance, workshop mark, assignment 1 mark, final exam mark, and overall course mark (which includes a component from quizzes held in workshops) for some course. We want to establish if there is any relationship between students’ attendance in workshops, performance in given assessment tasks, and the overall marks they get in the course. The data in the table gives the number of workshops students attended (/12 workshops), their mark from workshop quizzes (/10 marks), their mark in their first assignment (/50 marks), their mark in their exam (/48 marks), and their overall course mark (/100%). a) Using regression, establish a linear relation between attendance (x-axis) and each of the marks (y-axis) and fill the table below. Include a scatter plot of overall mark against attendance, including the regression line of best fit. [15 marks] Data R 2 Slope i.e. m Error in slope y - intercept i.e. c Error in y- intercept Residual standard error Workshop Assignmen t 1 Exam Overall b) Is a student's mark in Assignment 1 a useful indicator of how well they are likely to perform in the exam? Include relevant plot and briefly (in one or two sentences), explain your reasoning [5 marks] Page 7 of 8 Enter your answer here and fill the table above, expand the text box as needed. Enter your answer here, expand the text box as needed.

1015SCG Quantitative Reasoning Maths and inference assignment c) How many workshops does the student has to attend to pass the course (this means getting overall mark >=50%)? What is the error in the number of workshops? [7 marks] d) Using the regression model, on average, what is the change in overall course mark for each additional workshop a student attended, with an error range? Explain. [3 marks] Page 8 of 8 Enter your answer here, expand the text box as needed. Enter your answer here, expand the text box as needed.