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AP Statistics review Flashcards

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7988474098calculate IQR; anything above Q3+1.5(IQR) or below Q1-1.5(IQR) is an outlierHow do you check if there is outliers?0
7988474099median; it is resistant to skews and outliersIf a graph is skewed, should we calculate the median or the mean? Why?1
7988474100mean; generally is more accurate if the data has no outliersIf a graph is roughly symmetrical, should we calculate the median or the mean? Why?2
7988474101Minimum, Q1, Median, Q3, MaximumWhat is in the five number summary?3
7988474102variance=(standard deviation)^2Relationship between variance and standard deviation?4
7988474103the variance is roughly the average of the squared differences between each observation and the meanvariance definition5
7988474104the standard deviation is the square root of the variancestandard deviation6
7988474105IQRWhat should we use to measure spread if the median was calculated?7
7988474106standard deviationWhat should we use to measure spread if the mean was calculated?8
7988474107Q3-Q1; 50%What is the IQR? How much of the data does it represent?9
79884741081. Type data into L1 2. Find mean with 1 Variable Stats 3. Turn L2 into (L1-mean) 4. Turn L3 into (L2)^2 5. Go to 2nd STAT over to MATH, select sum( 6. Type in L3 7. multiply it by (1/n-1) 8. Square root itHow do you calculate standard deviation?10
7988474109What is the formula for standard deviation?11
7988474110Categorical: individuals can be assigned to one of several groups or categories Quantitative: takes numberical valuesCategorical variables vs. Quantitative Variables12
7988474111NoIf a possible outlier is on the fence, is it an outlier?13
7988474112Center (Mean or Median), Unusual Gaps or Outliers, Spread (Standard Deviation or IQR), Shape (Roughly Symmetric, slightly/heavily skewed left or right, bimodal, range)Things to include when describing a distribution14
7988474113Subtract the distribution mean and then divide by standard deviation. Tells us how many standard deviations from the mean an observation falls, and in what direction.Explain how to standardize a variable. What is the purpose of standardizing a variable?15
7988474114shape would be the same as the original distribution, the mean would become 0, the standard deviation would become 1What effect does standardizing the values have on the distribution?16
7988474115a curve that (a) is on or above the horizontal axis, and (b) has exactly an area of 1What is a density curve?17
7988474116when you want to find the percentile: invNorm (area, mean, standard deviation)Inverse Norm18
7988474117(x-mean)/standard deviationz19
7988474118the value with p percent observations less than ispth percentile20
7988474119can be used to describe the position of an individual within a distribution or to locate a specified percentile of the distributioncumulative relative frequency graph21
7988474120STAT plot, scatter, L1 and L2 (Plot 1: ON); STAT --> CALC --> 8:LinReg(a+bx) No r? --> 2nd 0 (Catalog) down to Diagnostic ONHow to find and interpret the correlation coefficient r for a scatterplot22
7988474121tells us the strength of a LINEAR association. -1 to 1. Not resistant to outliersr23
7988474122the proportion (percent) of the variation in the values of y that can be accounted for by the least squares regression liner^224
7988474123a scatterplot of the residuals against the explanatory variable. Residual plots help us assess how well a regression line fits the data. It should have NO PATTERNresidual plot25
7988474124a line that describes how a response variable y changes as an explanatory variable x changes. We often use a regression line to predict the value of y for a given value of x.regression line26
7988474125residual=y-y(hat) aka observed y - predicted yresidual formula27
7988474126BINS: 1. Binary: There only two outcomes (success and failure) 2. Independent: The events independent of one another? 3. Number: There is a fixed number of trials 4. Success: The probability of success equal in each trialWhat method do you use to check if a distribution or probability is binomial?28
7988474127BITS: 1. Binary: There only two outcomes (success and failure) 2. Independent: The events independent of one another 3. Trials: There is not a fixed number of trials 4. Success: The probability of success equal in each trialWhat method do you use to check if a distribution or probability is geometric?29
7988474128number of trialsn30
7988474129probability of successp31
7988474130number of successesk32
7988474131(n choose k) p^k (1-p)^(n-k)Binomial Formula for P(X=k)33
7988474132binompdf(n,p,k)Binomial Calculator Function to find P(X=k)34
7988474133binomcdf(n,p,k)Binomial Calculator Function for P(X≤k)35
79884741341-binomcdf(n,p,k-1)Binomial Calculator Function for P(X≥k)36
7988474135npmean of a binomial distribution37
7988474136√(np(1-p))standard deviation of a binomial distribution38
7988474137(1-p)^(k-1) x pGeometric Formula for P(X=k)39
7988474138geometpdf(p,k)Geometric Calculator Function to find P(X=k)40
7988474139geometcdf(p,k)Geometric Calculator Function for P(X≤k)41
79884741401-geometcdf(p,k-1)Geometric Calculator Function for P(X≥k)42
79884741411/p=expected number of trials until successMean of a geometric distribution43
7988474142√((1-p)/(p²))Standard deviation of a geometric distribution44
7988474143Take binomcdf(n,p,maximum) - binomcdf(n,p,minimum-1)What do you do if the binomial probability is for a range, rather than a specific number?45
7988474144type "n" on home screen, go to MATH --> PRB --> 3: ncr, type "k"how do you enter n choose k into the calculator?46
7988474145Measures of center (median and mean). Does NOT affect measures of spread (IQR and Standard Deviation) or shape.What does adding or subtracting a constant effect?47
7988474146Both measures of center (median and mean) and measures of spread (IQR and standard deviation). Shape is not effected. For variance, multiply by a² (if y=ax+b).What does multiplying or dividing a constant effect?48
7988474147√(σ²x+σ²y) --> you add to get the difference because variance is distance from mean and you cannot have a negative distanceσ(x-y)49
7988474148X1P1+X2P2+.... XKPK (SigmaXKPK)calculate μx by hand50
7988474149(X1-μx)²p(1)+(X2-μx)²p(2)+.... (Sigma(Xk-μx)²p(k))calculate var(x) by hand51
7988474150square root of varianceStandard deviation52
7988474151a fixed set of possible x values (whole numbers)discrete random variables53
7988474152-x takes all values in an interval of numbers -can be represented by a density curve (area of 1, on or above the horizontal axis)continuous random variables54
7988474153(σx)²+(σy)², but ONLY if x and y are independent.What is the variance of the sum of 2 random variables X and Y?55
7988474154no outcomes in commonmutually exclusive56
7988474155P(A)+P(B)addition rule for mutually exclusive events P (A U B)57
79884741561-P(A)complement rule P(A^C)58
7988474157P(A)+P(B)-P(A n B)general addition rule (not mutually exclusive) P(A U B)59
7988474158both A and B will occurintersection P(A n B)60
7988474159P(A n B) / P(B)conditional probability P (A | B)61
7988474160P(A) = P(A|B) P(B)= P(B|A)independent events (how to check independence)62
7988474161P(A) x P(B)multiplication rule for independent events P(A n B)63
7988474162P(A) x P(B|A)general multiplication rule (non-independent events) P(A n B)64
7988474163a list of possible outcomessample space65
7988474164a description of some chance process that consists of 2 parts: a sample space S and a probability for each outcomeprobability model66
7988474165any collection of outcomes from some chance process, designated by a capital letter (an event is a subset of the sample space)event67
7988474166P(A) = (number of outcomes corresponding to event A)/(total number of outcomes in sample space)What is the P(A) if all outcomes in the sample space are equally likely?68
7988474167probability that an event does not occurComplement69
79884741681What is the sum of the probabilities of all possible outcomes?70
7988474169P(A U B)= P(A)+P(B)What is the probability of two mutually exclusive events?71
79884741701. for event A, 0≤P(A)≤1 2. P(S)=1 3. If all outcomes in the sample space are equally likely, P(A)=number of outcomes corresponding to event A / total number of outcomes in sample space 4. P(A^C) = 1-P(A) 5. If A and B are mutually exclusive, P(A n B)=P(A)+P(B)five basic probability rules72
7988474171displays the sample space for probabilities involving two events more clearlyWhen is a two-way table helpful73
7988474172could have either event or bothIn statistics, what is meant by the word "or"?74
7988474173visually represents the probabilities of not mutually exclusive eventsWhen can a Venn Diagram be helpful?75
7988474174If A and B are any two events resulting from some chance process, then the probability of A or B (or both) is P(A U B)= P(A)+P(B)-P(A n B)What is the general addition rule for two events?76
7988474175both event A and event B occurWhat does the intersection of two or more events mean?77
7988474176either event A or event B (or both) occursWhat does the union of two or more events mean?78
7988474177If we observe more and more repetitions of any chance process, the proportion of times that a specific outcome occurs approaches a single value, which we can call the probability of that outcomeWhat is the law of large numbers?79
7988474178is a number between 0 and 1 that describes the proportion of times the outcome would occur in a very long series of repetitionsthe probability of any outcome...80
7988474179We interpret probability to represent the most accurate results if we did an infinite amount of trialsHow do you interpret a probability?81
79884741801. Short-run regularity --> the idea that probability is predictable in the short run 2. Law of Averages --> people except the alternative outcome to follow a different outcomeWhat are the two myths about randomness?82
7988474181the imitation of chance behavior, based on a model that accurately reflects the situationsimulation83
79884741821. State: What is the question of interest about some chance process 2. Plan: Describe how to use a chance device to imitate one repetition of process; clearly identify outcomes and measured variables 3. Do: Perform many repetitions of the simulation 4. Conclude: results to answer question of interestName and describe the four steps in performing a simulation84
7988474183not providing a clear description of the simulation process for the reader to replicate the simulationWhat are some common errors when using a table of random digits?85
7988474184both event A and event B occurWhat does the intersection of two or more events mean?86
7988474185The part of the population from which we actually collect information. We use information from a sample to draw conclusions about the entire populationsample87
7988474186In a statistical study, this is the entire group of individuals about which we want informationpopulation88
7988474187A study that uses an organized plan to choose a sample that represents some specific population. We base conclusions about the population on data from the sample.sample survey89
7988474188A sample selected by taking the members of the population that are easiest to reach; particularly prone to large bias.convenience sample90
7988474189The design of a statistical study shows ______ if it systematically favors certain outcomes.bias91
7988474190People decide whether to join a sample based on an open invitation; particularly prone to large bias.voluntary response sample92
7988474191The use of chance to select a sample; is the central principle of statistical sampling.random sampling93
7988474192every set of n individuals has an equal chance to be the sample actually selectedsimple random sample (SRS)94
7988474193Groups of individuals in a population that are similar in some way that might affect their responses.strata95
7988474194To select this type of sample, first classify the population into groups of similar individuals, called strata. Then choose a separate SRS from each stratum to form the full sample.stratified random sample96
7988474195To take this type of sample, first divide the population into smaller groups. Ideally, these groups should mirror the characteristics of the population. Then choose an SRS of the groups. All individuals in the chosen groups are included in the sample.cluster sample97
7988474196Drawing conclusions that go beyond the data at hand.inference98
7988474197Tells how close the estimate tends to be to the unknown parameter in repeated random sampling.margin of error99
7988474198The list from which a sample is actually chosen.sampling frame100
7988474199Occurs when some members of the population are left out of the sampling frame; a type of sampling error.undercoverage101
7988474200Occurs when a selected individual cannot be contacted or refuses to cooperate; an example of a nonsampling error.nonresponse102
7988474201The most important influence on the answers given to a survey. Confusing or leading questions can introduce strong bias, and changes in wording can greatly change a survey's outcome. Even the order in which questions are asked matters.wording of questions103
7988474202Observes individuals and measures variables of interest but does not attempt to influence the responses.observational study104
7988474203Deliberately imposes some treatment on individuals to measure their responses.experiment105
7988474204A variable that helps explain or influences changes in a response variable.explanatory variable106
7988474205A variable that measures an outcome of a study.response variable107
7988474206a variable that is not among the explanatory or response variables in a study but that may influence the response variable.lurking variable108
7988474207A specific condition applied to the individuals in an experiment. If an experiment has several explanatory variables, a treatment is a combination of specific values of these variables.treatment109
7988474208the smallest collection of individuals to which treatments are applied.experimental unit110
7988474209Experimental units that are human beings.subjects111
7988474210the explanatory variables in an experiment are often called thisfactors112
7988474211An important experimental design principle. Use some chance process to assign experimental units to treatments. This helps create roughly equivalent groups of experimental units by balancing the effects of lurking variables that aren't controlled on the treatment groups.random assignment113
7988474212An important experimental design principle. Use enough experimental units in each group so that any differences in the effects of the treatments can be distinguished from chance differences between the groups.replication114
7988474213An experiment in which neither the subjects nor those who interact with them and measure the response variable know which treatment a subject received.double-blind115
7988474214An experiment in which either the subjects or those who interact with them and measure the response variable, but not both, know which treatment a subject received.single-blind116
7988474215an inactive (fake) treatmentplacebo117
7988474216Describes the fact that some subjects respond favorably to any treatment, even an inactive oneplacebo effect118
7988474217A group of experimental units that are known before the experiment to be similar in some way that is expected to affect the response to the treatments.block119
7988474218Using information from a sample to draw conclusions about the larger population. Requires that the individuals taking part in a study be randomly selected from the population of interest.inference about the population120
7988474219Using the results of an experiment to conclude that the treatments caused the difference in responses. Requires a well-designed experiment in which the treatments are randomly assigned to the experimental units.inference about cause and effect121
7988474220When the treatments, the subjects, or the environment of an experiment are not realistic. Lack of realism can limit researchers' ability to apply the conclusions of an experiment to the settings of greatest interest.lack of realism122
7988474221A basic principle of data ethics. All planned studies must be approved in advance and monitored by _____________ charged with protecting the safety and well-being of the participants.institutional review board123
7988474222A basic principle of data ethics. Individuals must be informed in advance about the nature of a study and any risk of harm it may bring. Participating individuals must then consent in writing.informed consent124
7988474223a model of random eventssimulation125
7988474224a sample that includes the entire populationcensus126
7988474225a number that measures a characteristic of a populationpopulation parameter127
7988474226every fifth individual, for example, is chosensystematic sample128
7988474227a sampling design where several sampling methods are combinedmultistage sample129
7988474228the naturally occurring variability found in samplessampling variability130
7988474229the values that the experimenter used for a factorlevels131
7988474230control, randomization, replication, and blockingthe four principles of experimental design132
7988474231a design where all experimental units have an equal chance of receiving any treatmentcompletely randomized design133
7988474232if the true mean/proportion of the population is (null), the probability of getting a sample mean/proportion of _____ is (p-value).interpreting p value134
7988474233center: p1-p2 shape: n1p1, n1(1-p1), n2p2, and n2(1-p2) ≥ 10 spread (if 10% condition checks): √((p1(1-p1)/n1)+(p2(1-p2)/n2)p̂1-p̂2 center, shape, and spread135
7988474234plug in center and spread into bell curve, find probabilityprobability of getting a certain p̂1-p̂2 (ex. less than .1)136
7988474235(p̂1-p̂2) plus or minus z*(√((p1(1-p1)/n1)+(p2(1-p2)/n2))Confidence intervals for difference in proportions formula137
7988474236t for mean z for proportionsWhen do you use t and z test/intervals?138
7988474237Significance test for difference in proportions139
7988474238What is being claimed. Statistical test designed to assess strength of evidence against null hypothesis. Abbreviated by Ho.What is a null hypothesis?140
7988474239the claim about the population that we are trying to find evidence FOR, abbreviated by HaWhat is an alternative hypothesis?141
7988474240Ha less than or greater thanWhen is the alternative hypothesis one-sided?142
7988474241Ha is not equal toWhen is the alternative hypothesis two-sided?143
7988474242fixed value that we compare with the P-value, matter of judgement to determine if something is "statistically significant".What is a significance level?144
7988474243α=.05What is the default significance level?145
7988474244if the true mean/proportion of the population is (null), the probability of getting a sample mean/proportion of _____ is (p-value).Interpreting the p-value146
7988474245We reject our null hypothesis. There is sufficient evidence to say that (Ha) is true.p value ≤ α147
7988474246We fail to reject our null hypothesis. There is insufficient evidence to say that (Ho) is not true.p value ≥ α148
7988474247Type I Errorreject Ho when it is actually true149
7988474248Type II Errorfail to reject Ho when it is actually false150
7988474249probability of rejecting Ho when it is falsePower definition151
7988474250αprobability of Type I Error152
79884742511-powerprobability of Type II Error153
7988474252increase sample size/significance level αtwo ways to increase power154
7988474253State --> Ho/Ha, define parameter Plan --> one sample, z test Check --> random/normal/independent Do --> find p hat, find test statistic (z), use test statistic to find p-value Conclude --> p value ≤ α reject Ho p value ≥ α fail to reject Ho5 step process: z/t test155
7988474254Formula for test statistic (μ)156
7988474255(p̂-p)/(√((p)(1-p))/n)Formula for test statistic (p̂) (where p represents the null)157
7988474256overlap normal distribution for null and true. Find rejection line. Use normalcdfprobability of a Type II Error?158
7988474257for proportionswhen do you use z tests?159
7988474258for mean (population standard deviation unknown)when do you use t tests?160
7988474259tcdf(min, max, df)finding p value for t tests161
7988474260state--> Ho: μ1-μ2=0 (if its difference) plan --> one sample, paired t test check --> random, normal, independent do --> find test statistic and p value conclude --> normal conclusionSample paired t test162
7988474261The sample mean/proportion is far enough away from the true mean/proportion that it couldn't have happened by chanceWhat does statistically significant mean in context of a problem?163
7988474262check the differences histogram (μ1-μ2)When doing a paired t-test, to check normality, what do you do?164
7988474263In C% of all possible samples of size n, we will construct an interval that captures the true parameter (in context).How to interpret a C% Confidence Level165
7988474264We are C% confident that the interval (_,_) will capture the true parameter (in context).How to interpret a C% Confidence Interval166
7988474265random, normal, independentWhat conditions must be checked before constructing a confidence interval?167
7988474266State: Construct a C% confidence interval to estimate... Plan: one sample z-interval for proportions Check: Random, Normal, Independent Do: Find the standard error and z*, then p hat +/- z* Conclude: We are C% confident that the interval (_,_) will capture the true parameter (in context).C% confidence intervals of sample proportions, 5 step process168
7988474267What's the z interval standard error formula?169
7988474268InvNorm(#)How do you find z*?170
7988474269subtract the max and min confidence interval, divide it by two (aka find the mean of the interval ends)How do you find the point estimate of a sample?171
7988474270Ask, "What am I adding or subtracting from the point estimate?" So find the point estimate, then find the difference between the point estimate and the interval endsHow do you find the margin of error, given the confidence interval?172
7988474271use p hat=.5Finding sample size proportions: When p hat is unknown, or you want to guarantee a margin of error less than or equal to:173
7988474272x bar +/- z*(σ/√n)Finding the confidence interval when the standard deviation of the population is *known*174
7988474273starts normal or CLTChecking normal condition for z* (population standard deviation known)175
7988474274x bar +/- t*(Sx/√n)Finding the confidence interval when the standard deviation of the population is *unknown* (which is almost always true)176
7988474275n-1degrees of freedom177
7988474276InvT(area to the left, df)How do you find t*?178
7988474277same as standard deviation, but we call it "standard error" because we plugged in p hat for p (we are estimating)What is the standard error?179
7988474278provides an estimate of a population parameter.a point estimator is a statistic that...180
7988474279Confidence level C decreases, sample size n increasesExplain the two conditions when the margin of error gets smaller.181
7988474280NO; the confidence interval gives us a set of plausible values for the parameterDoes the confidence level tell us the chance that a particular confidence interval captures the population parameter?182
7988474281Sx is for a sample, σx is for a populationSx and σx: which is which?183
7988474282you are not given the population standard deviationHow do we know when do use a t* interval instead of a z interval?184
7988474283Normal for sample size... -n -n<15: if the data appears closely normal (roughly symmetric, single peak, no outliers)Checking normal condition for t* (population standard deviation unknown)185
7988474284plug data into List 1, look at histogram. Conclude with "The histogram looks roughly symmetric, so we should be safe to use the t distribution)How to check if a distribution is normal for t*, population n<15186
7988474285State: Construct a __% confidence interval to estimate... Plan: one sample t interval for a population mean Check: Random, Normal, Independent (for Normal, look at sample size and go from there) Do: Find the standard error (Sx/√n) and t*, then do x bar +/- t*(standard error) Conclude: We are __% confident that the interval (_,_) will capture the true parameter (in context).t* confidence interval, 5 step process187
7988474286z* or t* (standard error)margin of error formula188
7988474287x bar plus or minus t* (Sx/√n) -get x bar and Sx using 1 Var Stats -t*=Invt(area to the left, df) -population (n) will be givenWhen calculating t interval, what is it and where do you find the data?189
7988474288z/t* intervalWhat is it looking for if it asks for the appropriate critical value?190

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