322 Final BST Exam 2023 Graded A Questions And Answers

Statistics - The most important goal of statistics is to infer an unknown quantity (e.g., height of a species of plant) of an entire population of plants based on sample data (a subset of observations from the population) Population - Entire collection of individual units that share a property or sets of properties from which you want to generalize knowledge about unknown quantities (observations) based on a sub-set of individual units (sample). Parameter - a quantity describing a statistical population estimate or statistic - a related quantity calculated from a sample. Variable - any characteristic, number, or quantity that can be measured or counted. Height, weight, age, gender, business income and expenses, country of birth, capital expenditure, class grades and eye color are examples of variables. Observation units or Statistical units - the entity on which information is logged (e.g., one individual lake trout). Observation - contains all the values for the variables of interest such as the fork length and individual weight of an individual brook trout Categorical variables (qualitative variables) - describe membership in a category or group; characteristics of observations that do not have magnitude on a numerical scale nominal or ordinal Nominal - Survival (alive or dead) Method of disease transmission (e.g., water, air, animal vector) Eye colours (amber, blue, brown, gray, green, hazel, or red), Breed of a dog (e.g., collie, shepherd, terrier) Ordinal - Life stage (e.g., egg, larva, juvenile, adult) Snake bite severity score (e.g., minimal, moderate, severe), Size class (e.g., small, medium, large). Numerical Variables (Quantitative) - characteristics of observations have magnitude on a numerical scale. continuous or discrete Continuous - (can take any real-number value) Core body temperature (e.g., degrees Celcius, oC) Territory size of a bird (e.g., hectares) Size of fish (e.g., cm), Discrete - (only take indivisible units) Age at death (e.g., years) Number of amino acids in a protein, Number of eggs in a bird nest. statistical variables - variables are not based on their measuring units but rather their types Arm length and leg length can be both measured in centimeters but they are TWO different variables. Random Sampling - two criteria: Every observational unit in the population have an equal chance of being included in the sample. The selection of observational units in the population must be independent. EQUAL CHANCE AND INDEPENDENT Random sampling minimizes bias of estimates in relation to a parameter Experimental Study - Researcher randomly assigns observational units (fish individuals) to different groups (often called treatments; e.g., high/low protein diet) Observation Study - Researcher has no control over which observational units fall into which groups. Bar graph - Vertical or horizontal columns (bars) representing the distribution of a numerical variable against one or more categorical variables Explainatory variable - predicts or affects the other variable, called the response variable. When conducting an experiment, the treatment variable (the one manipulated by the researcher) is the explanatory variable response variable - the explanatory variable, predicts or affects the other variable, called the response variable. the measured effect of the treatment is the response variable. How many intervals (classes of abundance) should be used? - The Sturges' rule: vals=1+ln(n)/ln(2) HISTOGRAM - are important because they describe shape of numerical variables the mode - is the interval corresponding to the highest peak in the frequency distribution. A distribution is said bimodal when it has two dominant peaks the skew - refers to asymmetry in the shape of a frequency distribution for a numerical variable. (can be skewed left or right) frequency distribution - is a representation either in a graphical or tabular format, that displays the number of observations within a given internal of a quantitative variable. (continuous or discrete) intervals must be - mutually exclusive (each observation only belongs to one interval) and exhaustive (all observations must be included), and the interval size depends on the data being analyzed and the goals of the analys how to calculate intervals and speed intervals with 8 observations - Intervals: surges rule = 1+In(n)/ln(2) Here = 1 + ln(8)/ln(2) = 4 classes Speed intervals = (max(value)-min(value))/number of classes = (2-9) / 4 = 0.275 what does this mean (a,b] and [a,b) - (a,b] left open and right closed (starts from the right) [a,b) right open and left closed (starts from the left) location - The location tells us something about the average or typical individual (i.e., where the observations are centered). spread - The spread tells us how variable the measurements are from individual to individual - how widely scattered the observations are around the center. mean (Y) - sum of all observations in a sample divided by n, the number of observations standard deviation (s) - is a commonly used measure of the spread of a distribution. It measures how far from the mean the observations typically are. The standard deviation is large if most observations are far from the mean, and it is small if most measurements lie close to the mean.