Note:
- This project is simple. Because we are on distance online learning, we will be using EXCEL to obtain scatter plot, least regression line…etc, and perform simple operation to answer questions. Please use full sentences to answer questions. Questions (a), (d), and (g) are comprehensive. Please, refer to the PowerPoint presentation or the text book to answer them.
All papers must be typed. Please answer all the questions to get full credits.Cover page
is required,titles,label axes, questions numbering.
S.Djari 2022 MAT 120 PROJECT: American Black Bear (Lecture 4) American Black Bears: The American black bear ( Ursus Americanus) is one of the eight bear species in the world. It is the smallest North American bear and the most common bear species on the planet. In 1969 =, Dr. Michael R. Pelton of the University of Tennessee initiated a long-term study of the population in the Great Smoky Mountains National Park. One aspect of the study was to develop a model that could be used to predict a bear’s weight (since it is not practical to weigh bears in the field). One variable thought to be related to weight is the length of the bear. The following data represent the lengths and weight of 12 American black bears. Total Length (cm) Weight (kg) Total Length(cm) Weight (kg) 139.0 110 141.0 95 138.0 60 150.0 85 139.0 90 166.0 155 120.5 60 151.5 140 149.0 85 129.5 105 141.0 100 150.0 110 (a) Which variable is explanatory variable based on the goals of the research? (b) Draw a scatter diagram of the data. (c) Determine the linear correlation coefficient (Pearson’s) between weight and height. (d) Does a linear relation exist between the weight of the bear and its height? (e) Find the least-squares regression line, treating total length as explanatory and weight as the response variable. (f) Suppose a 149.0 cm bear is captured in the field. Use the least-squares regression line to predict the weight of the bear. (g) Interpret the slope and y-intercept if appropriate. Note: 1) This project is simple. Because we are on distance online learning, we will be using EXCEL to obtain scatter plot, least regression line…etc, and perform simple operation to answer questions. Please use full sentences to answer questions. Questions (a), (d), and (g) are comprehensive. Please, refer to the PowerPoint presentation or the text book to answer them. 2) All papers must be typed. Please answer all the questions to get full credits. Cover page is required, titles, label axes, questions numbering. 3) I will have 30 minutes on Wednesday 1/25/2022 after the lecture for instructions and graph (scattered plot, least regression line, and obtaining linear correlation coefficient) on Excel (recorded). Due Date: The due date for the project is no Later than February 6, 2022. After correcting your paper, I will ask you to make changes if necessary and submit it on eprotfolio for grade improvement. Final submission on eportfolio is due on February 13, 2022. Please do not submit on eportfolio without getting feedback. Chapter 2 Copyright © 2013, 2010 and 2007 Pearson Education, Inc. Chapter Organizing and Summarizing Data 2 Copyright © 2013, 2010 and 2007 Pearson Education, Inc. Section Organizing Qualitative Data 2.1 Copyright © 2013, 2010 and 2007 Pearson Education, Inc. Objectives Organize Qualitative Data in Tables Construct Bar Graphs Construct Pie Charts * * Copyright © 2013, 2010 and 2007 Pearson Education, Inc. 2-* When data is collected from a survey or designed experiment, they must be organized into a manageable form. Data that is not organized is referred to as raw data. Ways to Organize Data Tables Graphs Numerical Summaries (Chapter 3) * * Copyright © 2013, 2010 and 2007 Pearson Education, Inc. 2-* Objective 1 Organize Qualitative Data in Tables * * Copyright © 2013, 2010 and 2007 Pearson Education, Inc. 2-* A frequency distribution lists each category of data and the number of occurrences for each category of data. 3,3,4,5,1,4,2,3,3 * * Copyright © 2013, 2010 and 2007 Pearson Education, Inc. 2-* EXAMPLE Organizing Qualitative Data into a Frequency Distribution The data on the next slide represent the color of M&Ms in a bag of plain M&Ms. Construct a frequency distribution of the color of plain M&Ms. * * Copyright © 2013, 2010 and 2007 Pearson Education, Inc. 2-* EXAMPLE Organizing Qualitative Data into a Frequency Distribution brown, brown, yellow, red, red, red, brown, orange, blue, green, blue, brown, yellow, yellow, brown, red, red, brown, brown, brown, green, blue, green, orange, orange, yellow, yellow, yellow, red, brown, red, brown, orange, green, red, brown, yellow, orange, red, green, yellow, yellow, brown, yellow, orange * * Copyright © 2013, 2010 and 2007 Pearson Education, Inc. 2-* Frequency table ColorTallyFrequency Brown||||| ||||| ||12 Yellow||||| |||||10 Red||||| ||||9 Orange||||| |6 Blue|||3 Green|||||5 * * Copyright © 2013, 2010 and 2007 Pearson Education, Inc. 2-* The relative frequency is the proportion (or percent) of observations within a category and is found using the formula: A relative frequency distribution lists each category of data with the relative frequency. * * Copyright © 2013, 2010 and 2007 Pearson Education, Inc. 2-* EXAMPLE Organizing Qualitative Data into a Relative Frequency Distribution Use the frequency distribution obtained in the prior example to construct a relative frequency distribution of the color of plain M&Ms. * * Copyright © 2013, 2010 and 2007 Pearson Education, Inc. 2-* Frequency table ColorTallyFrequency Brown||||| ||||| ||12 Yellow||||| |||||10 Red||||| ||||9 Orange||||| |6 Blue|||3 Green|||||5 * * Copyright © 2013, 2010 and 2007 Pearson Education, Inc. 2-* ColorTallyFrequencyRelative Frequency Brown||||| ||||| ||1212/45 ≈ 0.2647 Yellow||||| |||||100.2222 Red||||| ||||90.2 Orange||||| |60.1333 Blue|||30.0667 Green|||||50.1111 * * Copyright © 2013, 2010 and 2007 Pearson Education, Inc. 2-* Objective 2 Construct Bar Graphs * * Copyright © 2013, 2010 and 2007 Pearson Education, Inc. 2-* A bar graph is constructed by labeling each category of data on either the horizontal or vertical axis and the frequency or relative frequency of the category on the other axis. Rectangles of equal width are drawn for each category. The height of each rectangle represents the category’s frequency or relative frequency. * * Copyright © 2013, 2010 and 2007 Pearson Education, Inc. 2-* Use the M&M data to construct a frequency bar graph and a relative frequency bar graph. EXAMPLEConstructing a Frequency and Relative Frequency Bar Graph * * Copyright © 2013, 2010 and 2007 Pearson Education, Inc. 2-* Frequency table ColorTallyFrequency Brown||||| ||||| ||12 Yellow||||| |||||10 Red||||| ||||9 Orange||||| |6 Blue|||3 Green|||||5 * * Copyright © 2013, 2010 and 2007 Pearson Education, Inc. 2-* * * Copyright © 2013, 2010 and 2007 Pearson Education, Inc. 2-* ColorTallyFrequencyRelative Frequency Brown||||| ||||| ||1212/45 ≈ 0.2667 Yellow||||| |||||100.2222 Red||||| ||||90.2 Orange||||| |60.1333 Blue|||30.0667 Green|||||50.1111 * * Copyright © 2013, 2010 and 2007 Pearson Education, Inc. 2-* * * Copyright © 2013, 2010 and 2007 Pearson Education, Inc. 2-* A Pareto chart is a bar graph where the bars are drawn in decreasing order of frequency or relative frequency. * * Copyright © 2013, 2010 and 2007 Pearson Education, Inc. 2-* Pareto Chart * * Copyright © 2013, 2010 and 2007 Pearson Education, Inc. 2-* EXAMPLEComparing Two Data Sets The following data represent the marital status (in millions) of U.S. residents 18 years of age or older in 1990 and 2006. Draw a side-by-side relative frequency bar graph of the data. Marital Status19902006 Never married40.455.3 Married112.6127.7 Widowed13.813.9 Divorced15.122.8 * * Copyright © 2013, 2010 and 2007 Pearson Education, Inc. 2-* Relative Frequency Marital Status Marital Status in 1990 vs. 2006 1990 2006 * * Copyright © 2013, 2010 and 2007 Pearson Education, Inc. 2-* Objective 3 Construct Pie Charts * * Copyright © 2013, 2010 and 2007 Pearson Education, Inc. 2-* A pie chart is a circle divided into sectors. Each sector represents a category of data. The area of each sector is proportional to the frequency of the category. * * Copyright © 2013, 2010 and 2007 Pearson Education, Inc. 2-* EXAMPLEConstructing a Pie Chart The following data represent the marital status (in millions) of U.S. residents 18 years of age or older in 2006. Draw a pie chart of the data. Marital StatusFrequency Never married55.3 Married127.7 Widowed13.9 Divorced22.8 * * Copyright © 2013, 2010 and 2007 Pearson Education, Inc. 2-* EXAMPLEConstructing a Pie Chart * * Copyright © 2013, 2010 and 2007 Pearson Education, Inc. Section Organizing Quantitative Data: The Popular Displays 2.2 Copyright © 2013, 2010 and 2007 Pearson Education, Inc. 2-* Objectives Organize discrete data in tables Construct histograms of discrete data Organize continuous data in tables Construct histograms of continuous data Draw stem-and-leaf plots Draw dot plots Identify the shape of a distribution * * Copyright © 2013, 2010 and 2007 Pearson Education, Inc. 2-* The first step in summarizing quantitative data is to determine whether the data are discrete or continuous. If the data are discrete and there are relatively few different values of the variable, the categories of data (classes) will be the observations (as in qualitative data). If the data are discrete, but there are many different values of the variables, or if the data are continuous, the categories of data (the classes) must be created using intervals of numbers. * * Copyright © 2013, 2010 and 2007 Pearson Education, Inc. 2-* Objective 1 Organize Discrete Data in Tables * * Copyright © 2013, 2010 and 2007 Pearson Education, Inc. 2-* The following data represent the number of available cars in a household based on a random sample of 50 households. Construct a frequency and relative frequency distribution. EXAMPLE Constructing Frequency and Relative Frequency Distribution from Discrete Data 3012111202 4222122024 1132412122 3321220322 2321221135 Data based on results reported by the United States Bureau of the Census. * * Copyright © 2013, 2010 and 2007 Pearson Education, Inc. 2-* # of CarsTallyFrequencyRelative Frequency 0||||44/50 = 0.08 1||||| ||||| |||1313/50 = 0.26 2||||| ||||| ||||| ||||| ||220.44 3||||| ||70.14 4|||30.06 5|10.02 * * Copyright © 2013, 2010 and 2007 Pearson Education, Inc. 2-* Objective 2 Construct Histograms of Discrete Data * * Copyright © 2013, 2010 and 2007 Pearson Education, Inc. 2-*