WGU statistics Questions And Answers

The probability of any event is between one and o. What is the equation for this? - ANS For any event A, 0 ≤ P(A) ≤ 1. The sum of all possible probabilities is___? - ANS One, the equation is :P(S) = 1 What is the complement rule? or the probability that an event does not occur is 1 minus the probability that it does occur. - ANS P(not A) = 1 - P(A) In probability, "OR" means either one or the other or both. - ANS P(A or B) = P(event A occurs or event B occurs or both occur) Two events that cannot occur at the same time are called - ANS disjoint or mutually exclusive The Addition Rule for Disjoint Events: - ANS If A and B are disjoint events, then P(A or B) = P(A) + P(B). P(A and B) = - ANS P(event A occurs and event B occurs) The idea of disjoint events is - ANS is about whether or not it is possible for the events to occur at the same time The idea of independent events is about - ANS whether or not the events affect each other in the sense that the occurrence of one event affects the probability of the occurrence of the other If A and B Disjoint - ANS A and B can not be indepentdent If A and B are two independent events (Multiplication Rule) - ANS P(A and B) = P(A) * P(B). if A, B and C are three independent events, - ANS P(A and B and C) = P(A) * P(B) * P(C) The Complement Rule, - ANS P(A) = 1 - P(not A), P(L) = 1 - P(not L) = 1 - P(not O1 and not O2 and not O3 and not O4 and not O5 and not O6 and not O7 and not O8 and not O9 and not O10). - ANS Applying the Multiplication rule:Now, using the multiplication rule, = 1 - (.56 * .56 * .56 * .56 * .56 * .56 * .56 * .56 * .56 * .56) = 1 - .003 = .997. P(at least one person chosen has blood type O) - ANS P((O and O) or (O and not O) or (not O and O)) = (.44 * .44) + (.44 * .56) + (.56 * .44) = .6864. If A and B are disjoint events - - ANS P(A and B)= 0 The General Addition Rule states that for any two events, - ANS P(A or B) = P(A) + P(B) - P(A and B) When each of two outcomes has two possible values (yes/no), - ANS there are four possible combinations altogether, which correspond to the four possible outcomes. How do we build a two-way table of probabilities? - ANS Horizontally, A, not A and total, Vertically, B. not B and total In a two-way table of probabilities, what is the total of all outcomes (lower right corner?) - ANS 1 Two events A and B are independent if any one of the following hold: - ANS P(B | A) = P(B) P(A | B) = P(A) P(B | A) = P(B | not A) P(A and B) = P(A) * P(B) In general, another method for checking the independence of events A and B is to compare - ANS P(A and B) to P(A) * P(B). If the two are equal, then A and B are independent, otherwise the two are not independent. "one in every thousand people (0.001) of all individuals are infected with HIV (H) - give equasion - ANS P(H) = .001 If someone actually has HIV, the probability of testing positive is .95" (H) give equasion - ANS P(T | H) = .95 Use the General Multiplication Rule to find the probability that someone chosen at random from the population has HIV and tests positive. (H is HIV positive and probability of HIV+ test accuracy is .95) - ANS P(H and T) = P(H) * P(T given H) = .001 x .95 = .00095. IF person is HIV positive and test accuracy is .95, what are the chances that that person will test negative (give equation) - ANS P(not T | H) = 1 - P(T | H) = 1 - .95 = .05. In a probability tree, the probabilities in the first branch-off are - ANS non-conditional probabilities In a probability tree,second branch-off are - ANS conditional probabilities. In a probability tree, the second thing to note is that probabilities of branches that branch out from the same point always add up to - ANS one WGU statistics In a probability tree, symbolically, V = (C and V) or (not C and V). Thus, the overall probability of taking the vacation is - ANS P(V) = P( (C and V) or (not C and V) ). In a probability tree, overall probability of V, in the event of C or not C is determined by what sequence of equasions? - ANS Applying the Addition Rule for Disjoint Events, we have P(V) = P(C and V) + P(not C and V). Applying the General Multiplication Rule to each term, we have P(V) = P(C) * P(V | C) + P(not C) * P(V | not C) A histogram is a display of - ANS a single quantitative variable A scatterplot is a display of - ANS two quantitative variables A two way table is a display of - ANS the relationship of two variables that are both categorical The appropriate display for the relationship between two variables based upon their type (Quantitative or categorical) and their role (explanatory or response) is - ANS side by side box plots What are the two simple graphical displays for visualizing the distribution of categorical data? - ANS The pie chart and the bar chart How does one calculate the standard deviation? - ANS Square each of the deviations: then,Average the square deviations by adding them up, and dividing by n - 1, (one less than the sample size): By distribution of a variable, we mean - ANS what values the variable takes and how often the variable takes those values A pie chart is a display for - ANS visualizing the distribution of categorical data pictogram - ANS is a variation of a pie chart, but can be misleading The three displays for one quantitative variable are - ANS histogram, stemplot and box plot symetric distributions for one quantitative variable can be shaped in how many ways? - ANS Symmetric (unimodal), single peaked, Symmetric (Bimodal) Double peaked and Symmetric uniform distribution A right skew distribution - ANS has a tail that curves down to the right A left skewed distribution - ANS Has a tail which curves up to the left. Can skewed distribution be bimodal? - ANS yes Spread (Also called variability) - ANS can be described by the approximate range covered by the data. In stemplots, - ANS the leaf is the right-most digit The stem is everything but - ANS the right -most digit To make a stem plot - ANS 1. Separate each observation into a stem and a leaf 2. Write the stems in a vertical column with the smallest at the top and draw a vertical line at the right of this column 3. Go through the data points and write each leaf in a row to the right of the stem 4. rearrange the leaves in an increasing order A dotplot - ANS Is another type of display used to summarize a quantitative variable graphically. Mode - ANS the most commonly occurinng value in a dataset equation for mean - ANS a+b+c/3 (The denominator is always the number of variables added Median - ANS The midpoint of a distribution The Standard deviation - ANS calculate the mean. Calculate the difference between the mean and each observation and the mean. square each figure determined from the previous computation, Add up all the squared numbers and divide them by n(the total number of observations )-1. The Standard deviation rule for "the normal shape" bell curve. - ANS Apporximatlely 68% of the observations fall within 1 standard deviation, approx. 95% of the observations fall with 2 standard deviations of the mean. Approx. 99.7% (or virtually all) of the observation fall withim three standard deviations of the mean In case C→Q we compared - ANS distributions of the quantitative response. In case C→C we compared - ANS distributions of the categorical response. when creating a scatterplot, - ANS the explanatory variable should always be plotted on the horizontal X-axis, and the response variable should be plotted on the vertical Y-axis. If in a specific example we do not have a clear distinction between explanatory and response variables, each of the variables can be plotted on either axis. a positive scatter plot - ANS moves upward and relatively straight a negative scatterplot - ANS moves downward and relatively straight a neither positive or negative scatter plot can take on any number forms, even a U - ANS can take on any number of forms, even a U shape Side by side box plots are appropriate for comparing - ANS several groups of quantitative data A two way table compares - ANS two groups of categorical data A scatterplot compares - ANS two quantitative variables When determining quartiles in the range, the mid point is the - ANS median The first quartile is determined by - ANS Finding the median of the data's range, then finding the median of the first 50% IQR = (Interquartile Range) - ANS Q3-Q1 (Median of the third quartile minus the median of the second quartile The 1.5(IQR) Criterion for Outliers An observation is considered a suspected outlier if it is: - ANS below Q1 - 1.5(IQR) or above Q3 + 1.5(IQR) The IQR should be used as a measure of spread of a distribution only when - ANS the median is used as a measure of center. The five-number summary of a distribution consists of - ANS the median (M), the two quartiles (Q1, Q3) and the extremes (min, Max). The five-number summary provides a - ANS complete numerical description of a distribution. For a boxplot, the median describes the center, and the extremes (which give the range) and - ANS the quartiles (which give the IQR) describe the spread. The boxplot graphically represents - ANS the distribution of a quantitative variable by visually displaying the five number summary and any observation that was classified as a suspected outlier using the 1.5(IQR) criterion. Boxplots are most useful when presented - ANS side-by-side to compare and contrast distributions from two or more groups. The IQR should be paired - ANS as a measure of spread with the median as a measure of center. The idea behind the standard deviation is to - ANS quantify the spread of a distribution by measuring how far the observations are from their mean, x⎯⎯. Notation for standard deviation - ANS SD or s average of the squared deviations - ANS variance The standard deviation rule is also called - ANS the empirical rule. The value of r is such that - ANS -1 r +1. Positive correlation: (r) - ANS If x and y have a strong positive linear correlation, r is close to +1. An r value of exactly +1 indicates a perfect positive fit. Positive values indicate a relationship between x and y variables such that as values for x increases, values for y also increase. Negative correlation: (r) - ANS If x and y have a strong negative linear correlation, r is close to -1. An r value of exactly -1 indicates a perfect negative fit. Negative values indicate a relationship between x and y such that as values for x increase, values for y decrease. No correlation: (r) - ANS If there is no linear correlation or a weak linear correlation, r is close to 0. A value near zero means that there is a random, nonlinear relationship between the two variables Note that r is a dimensionless quantity; that is, it does not depend on the units employed. For r, perfect correlation of ± 1 occurs only when - ANS he data points all lie exactly on a straight line. If r = +1, the slope of this line is positive. If r = -1, the slope of this line is negative. For r, a correlation greater than 0.8 is generally described as - ANS strong For r, a correlation less than 0.5 is generally described as - ANS Equation for determining an outlier - ANS 1.5(IQR) = amount added to Q3 or Subtracted from Q1