Probability and Statistics Comprehensive Exam Questions And Complete Detailed Answers 100% Verified.

Uses of statistics - correct answer -Used to organize and summarize information -Used to determine exactly what conclusions are justified based on the results that were obtained Statistics: - correct answer set of mathematical procedures for organizing, summarizing and interpreting information Goals of statistical procedure - correct answer Accurate and meaningful interpretation Population - correct answer the set of all the individuals of interest in a particular study -always identified by the researcher Sample - correct answer -a set of individuals selected from a population, usually intended to represent the population in a research study. Variable - correct answer a characteristic or condition that changes or has different values for different individuals. -height, weight, gender, or personaility can me environmental conditions-temp, time of day, size of the room Data - correct answer Measurements or observations of a variable Data set- - correct answer a collection of measurements or observations Datum - correct answer a single measurement or observation -commonly called a a score or raw score Parameter - correct answer -A value, usually a numerical value, that describes a population. -Derived from measurements of the individuals in the population Statistic - correct answer -A value, usually a numerical value, that describes a sample -Derived from measurements of the individuals in the sample Descriptive Statistics - correct answer -Summarize data -Organize data -Simplify data -summarizes a set of scores by computing an average Examples- Tables, graphs, averages Inferential statistics - correct answer Study samples to make generalizations about the population Sampling error - correct answer -Sample is never identical to population -The discrepancy, or amount of error, that exists between a sample statistic and the corresponding population parameter Goal of Experimental method - correct answer To demonstrate a cause-and-effect relationship Manipulation - correct answer The level of one variable is determined by the experimenter -The reacher manipulates one variable by changing its value from one level to another -second variable is observed to determine whether the manipulation causes changes to occur Control - correct answer -rules out influence of other variables -exercise control over the research situation to ensure that other, extraneous variables do not influence the relationship being examined -Participant variables -Environmental variables Independent Variable - correct answer -variable manipulated by the researcher -is the Independent because no other variable in the study influences its value Dependent variable - correct answer is the one observed to assess the effect of treatment -Dependent because its value is thought to depend on the value of the independent variable Correlational Research - correct answer Inferential/Descriptive Statistic (r) -Describes strength of linear relation between two variables -Strength of relation = degree of association -Properties of r -Ranges between -1 and 1 inclusive -Sign (+ or -) gives direction of relation Disadvantages: correlation does not indicate causation Advantages: study variables that are not easily produced in the laboratory Constructs - correct answer -Internal attributes or characteristics that cannot be directly observed - Useful for describing and explaining behavior Operational Definition - correct answer -Identifies a measurement procedure for measuring an external behavior -Uses the resulting measurements as a definition and a measurement of a hypothetical construct Discrete variable - correct answer -Has separate, indivisible categories -No values can exist between two neighboring categories Continuous variable - correct answer -There are an infinite number of possible values between any two observed values. -Is divisible into an infinite number of parts Real Limits - correct answer -are the boundaries of intervals for scores of measured on a continuous number line. -The real limit separating two adjacent scores is exactly halfway between the scores. -The upper real limit is at the top of the interval -The lower real limit is at the bottom of the interval Nominal - correct answer Characteristics:Label and categorize No quantitative distinctions Examples:Gender Diagnosis Experimental or Control Ordinal - correct answer Characteristics:Categorizes observations Categories organized by size or magnitude Examples:Rank in class Clothing sizes (S,M,L,XL) Olympic medals Interval - correct answer Characteristics:Ordered categories Interval between categories of equal size Arbitrary or absent zero point Exact Temperature IQ Golf scores (above/below parmples: Ratio - correct answer Characteristics: Ordered categories Equal interval between categories Absolute zero point Examples.Number of correct answers Time to complete task Gain in height since last year Statistical Notation - correct answer Statistics uses some specific notation Scores are referred to as X (and Y) N is the number of scores in a population n is the number of scores in a sample Frequency Distribution - correct answer -An organized tabulation -Showing the number of individuals located in each category on the scale of measurement -Can be either a table or a graph -Always shows: -The categories that make up the scale -The frequency, or number of individuals, in each category Frequency Distribution Graphs - correct answer -Pictures of data available in tables -All have two axes - X-axis (abscissa) has categories of measurement scale increasing left to right -Y-axis (ordinate) has frequencies increasing bottom to top -General principles Both axes should have value 0 where they meet Graphs for Nominal or Ordinal Data - correct answer For non-numerical values (scores), a bar graph is used -Similar to a histogram -Spaces between adjacent bars indicates discrete categories without order (nominal) or of unmeasurable width (ordinal) Frequency Distribution Shape - correct answer -Symmetrical distribution: each side is a mirror image of the other -Skewed distribution: scores pile up on one side and taper off in a tail on the other -Tail on the right (high scores) = positive skew -Tail on the left (low scores) = negative skew Central tendency - correct answer -A statistical measure -A single score to define the center of a distribution - Purpose: find the single score that is most typical or best represents the entire group Mean - correct answer -Sum of the scores divided by the number of scores in the data -The balance point for the distribution -Defined by distances -Often is not the midpoint of the scores Weighted Mean - correct answer -Combine two sets of scores -Three steps: -Determine the combined sum of all the scores -Determine the combined number of scores -Divide the sum of scores by the total number of scores Median - correct answer -The median is the midpoint of the scores in a distribution when they are listed in order from smallest to largest. -The median divides the scores into two groups of equal size. -Defined by number of scores -Often is not the balance point of the scores Mean and Median - correct answer measure central tendency, using two different concepts of "middle" mode - correct answer - the score or category that has the greatest frequency of any in the frequency distribution -Can be used with any scale of measurement Symmetrical Distributions - correct answer -Central tendency and the shape of the distribution - Mean and median have same value -If exactly one mode, it has same value as the mean and the median -Distribution may have more than one mode, or no mode at all Variability - correct answer -A quantitative measure of the differences between scores -Describes the degree to which the scores are spread out or clustered together Variabilty Measures: - correct answer -Range -Standard deviation-most common and most important measure of variability -Variance Standard deviation and variance for a population - correct answer Most common and most important measure of variability -A measure of the standard, or average, distance from the mean -Describes whether the scores are clustered closely around the mean or are widely scattered Standard Deviation and variance for a sample - correct answer -Goal of inferential statistics: -Draw general conclusions about population -Based on limited information from a sample -Samples differ from the population -Samples have less variability -Computing the Variance and Standard Deviation in the same way as for a population would give a biased estimate of the population values Variance and Inferential Statistics - correct answer -Goal of inferential statistics is to detect meaningful and significant patterns in research results -Variability in the data influences how easy it is to see patterns -High variability obscures patterns that would be visible in low variability samples -Variability is sometimes called error variance Purpose of z-scores - correct answer -Identify and describe location of every score in the distribution -Standardize an entire distribution -Takes different distributions and makes them equivalent and comparable Z-Score Sign - correct answer tells whether score is located above or below the mean z-Score number - correct answer tells distance between score and mean in standard deviation units