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13560027090How do you check if there is outliers?calculate IQR; anything above Q3+1.5(IQR) or below Q1-1.5(IQR) is an outlier0
13560027091If a graph is skewed, should we calculate the median or the mean? Why?median; it is resistant to skews and outliers1
13560027092If a graph is roughly symmetrical, should we calculate the median or the mean? Why?mean; generally is more accurate if the data has no outliers2
13560027093What is in the five number summary?Minimum, Q1, Median, Q3, Maximum3
13560027094Relationship between variance and standard deviation?variance=(standard deviation)^24
13560027095variance definitionthe variance is roughly the average of the squared differences between each observation and the mean5
13560027096standard deviationthe standard deviation is the square root of the variance6
13560027097What should we use to measure spread if the median was calculated?IQR7
13560027098What should we use to measure spread if the mean was calculated?standard deviation8
13560027099What is the IQR? How much of the data does it represent?Q3-Q1; 50%9
13560027100How do you calculate standard deviation?1. 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 it10
13560027280What is the formula for standard deviation?11
13560027101Categorical variables vs. Quantitative VariablesCategorical: individuals can be assigned to one of several groups or categories Quantitative: takes numberical values12
13560027102If a possible outlier is on the fence, is it an outlier?No13
13560027103Things to include when describing a distributionCenter (Mean or Median), Unusual Gaps or Outliers, Spread (Standard Deviation or IQR), Shape (Roughly Symmetric, slightly/heavily skewed left or right, bimodal, range)14
13560027104Explain how to standardize a variable. What is the purpose of standardizing a variable?Subtract 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.15
13560027105What effect does standardizing the values have on the distribution?shape would be the same as the original distribution, the mean would become 0, the standard deviation would become 116
13560027106What is a density curve?a curve that (a) is on or above the horizontal axis, and (b) has exactly an area of 117
13560027107Inverse Normwhen you want to find the percentile: invNorm (area, mean, standard deviation)18
13560027108z(x-mean)/standard deviation19
13560027109pth percentilethe value with p percent observations less than is20
13560027110cumulative relative frequency graphcan be used to describe the position of an individual within a distribution or to locate a specified percentile of the distribution21
13560027111How to find and interpret the correlation coefficient r for a scatterplotSTAT plot, scatter, L1 and L2 (Plot 1: ON); STAT --> CALC --> 8:LinReg(a+bx) No r? --> 2nd 0 (Catalog) down to Diagnostic ON22
13560027112rtells us the strength of a LINEAR association. -1 to 1. Not resistant to outliers23
13560027113r^2the proportion (percent) of the variation in the values of y that can be accounted for by the least squares regression line24
13560027114residual plota 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 PATTERN25
13560027115regression linea 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.26
13560027116residual formularesidual=y-y(hat) aka observed y - predicted y27
13560027117What method do you use to check if a distribution or probability is binomial?BINS: 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 trial28
13560027118What method do you use to check if a distribution or probability is geometric?BITS: 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 trial29
13560027119nnumber of trials30
13560027120pprobability of success31
13560027121knumber of successes32
13560027122Binomial Formula for P(X=k)(n choose k) p^k (1-p)^(n-k)33
13560027123Binomial Calculator Function to find P(X=k)binompdf(n,p,k)34
13560027124Binomial Calculator Function for P(X≤k)binomcdf(n,p,k)35
13560027125Binomial Calculator Function for P(X≥k)1-binomcdf(n,p,k-1)36
13560027126mean of a binomial distributionnp37
13560027127standard deviation of a binomial distribution√(np(1-p))38
13560027128Geometric Formula for P(X=k)(1-p)^(k-1) x p39
13560027129Geometric Calculator Function to find P(X=k)geometpdf(p,k)40
13560027130Geometric Calculator Function for P(X≤k)geometcdf(p,k)41
13560027131Geometric Calculator Function for P(X≥k)1-geometcdf(p,k-1)42
13560027132Mean of a geometric distribution1/p=expected number of trials until success43
13560027133Standard deviation of a geometric distribution√((1-p)/(p²))44
13560027134What do you do if the binomial probability is for a range, rather than a specific number?Take binomcdf(n,p,maximum) - binomcdf(n,p,minimum-1)45
13560027135how do you enter n choose k into the calculator?type "n" on home screen, go to MATH --> PRB --> 3: ncr, type "k"46
13560027136μ(x+y)μx+μy47
13560027137μ(x-y)μx-μy48
13560027138σ(x+y)√(σ²x+σ²y)49
13560027139What does adding or subtracting a constant effect?Measures of center (median and mean). Does NOT affect measures of spread (IQR and Standard Deviation) or shape.50
13560027140What does multiplying or dividing a constant effect?Both 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).51
13560027141σ(x-y)√(σ²x+σ²y) --> you add to get the difference because variance is distance from mean and you cannot have a negative distance52
13560027142calculate μx by handX1P1+X2P2+.... XKPK (SigmaXKPK)53
13560027143calculate var(x) by hand(X1-μx)²p(1)+(X2-μx)²p(2)+.... (Sigma(Xk-μx)²p(k))54
13560027144Standard deviationsquare root of variance55
13560027145discrete random variablesa fixed set of possible x values (whole numbers)56
13560027146continuous random variables-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)57
13560027147What is the variance of the sum of 2 random variables X and Y?(σx)²+(σy)², but ONLY if x and y are independent.58
13560027148mutually exclusiveno outcomes in common59
13560027149addition rule for mutually exclusive events P (A U B)P(A)+P(B)60
13560027150complement rule P(A^C)1-P(A)61
13560027151general addition rule (not mutually exclusive) P(A U B)P(A)+P(B)-P(A n B)62
13560027152intersection P(A n B)both A and B will occur63
13560027153conditional probability P (A | B)P(A n B) / P(B)64
13560027154independent events (how to check independence)P(A) = P(A|B) P(B)= P(B|A)65
13560027155multiplication rule for independent events P(A n B)P(A) x P(B)66
13560027156general multiplication rule (non-independent events) P(A n B)P(A) x P(B|A)67
13560027157sample spacea list of possible outcomes68
13560027158probability modela description of some chance process that consists of 2 parts: a sample space S and a probability for each outcome69
13560027159eventany collection of outcomes from some chance process, designated by a capital letter (an event is a subset of the sample space)70
13560027160What is the P(A) 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)71
13560027161Complementprobability that an event does not occur72
13560027162What is the sum of the probabilities of all possible outcomes?173
13560027163What is the probability of two mutually exclusive events?P(A U B)= P(A)+P(B)74
13560027164five basic probability rules1. 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)75
13560027165When is a two-way table helpfuldisplays the sample space for probabilities involving two events more clearly76
13560027166In statistics, what is meant by the word "or"?could have either event or both77
13560027167When can a Venn Diagram be helpful?visually represents the probabilities of not mutually exclusive events78
13560027168What is the general addition rule for two events?If 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)79
13560027169What does the intersection of two or more events mean?both event A and event B occur80
13560027170What does the union of two or more events mean?either event A or event B (or both) occurs81
13560027171What is the law of large numbers?If 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 outcome82
13560027172the probability of any outcome...is a number between 0 and 1 that describes the proportion of times the outcome would occur in a very long series of repetitions83
13560027173How do you interpret a probability?We interpret probability to represent the most accurate results if we did an infinite amount of trials84
13560027174What are the two myths about randomness?1. 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 outcome85
13560027175simulationthe imitation of chance behavior, based on a model that accurately reflects the situation86
13560027176Name and describe the four steps in performing a simulation1. 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 interest87
13560027177What are some common errors when using a table of random digits?not providing a clear description of the simulation process for the reader to replicate the simulation88
13560027178What does the intersection of two or more events mean?both event A and event B occur89
13560027179sampleThe part of the population from which we actually collect information. We use information from a sample to draw conclusions about the entire population90
13560027180populationIn a statistical study, this is the entire group of individuals about which we want information91
13560027181sample surveyA 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.92
13560027182convenience sampleA sample selected by taking the members of the population that are easiest to reach; particularly prone to large bias.93
13560027183biasThe design of a statistical study shows ______ if it systematically favors certain outcomes.94
13560027184voluntary response samplePeople decide whether to join a sample based on an open invitation; particularly prone to large bias.95
13560027185random samplingThe use of chance to select a sample; is the central principle of statistical sampling.96
13560027186simple random sample (SRS)every set of n individuals has an equal chance to be the sample actually selected97
13560027187strataGroups of individuals in a population that are similar in some way that might affect their responses.98
13560027188stratified random sampleTo 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.99
13560027189cluster sampleTo 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.100
13560027190inferenceDrawing conclusions that go beyond the data at hand.101
13560027191margin of errorTells how close the estimate tends to be to the unknown parameter in repeated random sampling.102
13560027192sampling frameThe list from which a sample is actually chosen.103
13560027193undercoverageOccurs when some members of the population are left out of the sampling frame; a type of sampling error.104
13560027194nonresponseOccurs when a selected individual cannot be contacted or refuses to cooperate; an example of a nonsampling error.105
13560027195wording of questionsThe 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.106
13560027196observational studyObserves individuals and measures variables of interest but does not attempt to influence the responses.107
13560027197experimentDeliberately imposes some treatment on individuals to measure their responses.108
13560027198explanatory variableA variable that helps explain or influences changes in a response variable.109
13560027199response variableA variable that measures an outcome of a study.110
13560027200lurking variablea variable that is not among the explanatory or response variables in a study but that may influence the response variable.111
13560027201treatmentA 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.112
13560027202experimental unitthe smallest collection of individuals to which treatments are applied.113
13560027203subjectsExperimental units that are human beings.114
13560027204factorsthe explanatory variables in an experiment are often called this115
13560027205random assignmentAn 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.116
13560027206replicationAn 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.117
13560027207double-blindAn experiment in which neither the subjects nor those who interact with them and measure the response variable know which treatment a subject received.118
13560027208single-blindAn 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.119
13560027209placeboan inactive (fake) treatment120
13560027210placebo effectDescribes the fact that some subjects respond favorably to any treatment, even an inactive one121
13560027211blockA 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.122
13560027212inference about the populationUsing 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.123
13560027213inference about cause and effectUsing 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.124
13560027214lack of realismWhen 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.125
13560027215institutional review boardA 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.126
13560027216informed consentA 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.127
13560027217simulationa model of random events128
13560027218censusa sample that includes the entire population129
13560027219population parametera number that measures a characteristic of a population130
13560027220systematic sampleevery fifth individual, for example, is chosen131
13560027221multistage samplea sampling design where several sampling methods are combined132
13560027222sampling variabilitythe naturally occurring variability found in samples133
13560027223levelsthe values that the experimenter used for a factor134
13560027224the four principles of experimental designcontrol, randomization, replication, and blocking135
13560027225completely randomized designa design where all experimental units have an equal chance of receiving any treatment136
13560027226interpreting p valueif the true mean/proportion of the population is (null), the probability of getting a sample mean/proportion of _____ is (p-value).137
13560027227p̂1-p̂2 center, shape, and spreadcenter: 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)138
13560027228probability of getting a certain p̂1-p̂2 (ex. less than .1)plug in center and spread into bell curve, find probability139
13560027229Confidence intervals for difference in proportions formula(p̂1-p̂2) plus or minus z*(√((p1(1-p1)/n1)+(p2(1-p2)/n2))140
13560027230When do you use t and z test/intervals?t for mean z for proportions141
13560027281Significance test for difference in proportions142
13560027231What is a null hypothesis?What is being claimed. Statistical test designed to assess strength of evidence against null hypothesis. Abbreviated by Ho.143
13560027232What is an alternative hypothesis?the claim about the population that we are trying to find evidence FOR, abbreviated by Ha144
13560027233When is the alternative hypothesis one-sided?Ha less than or greater than145
13560027234When is the alternative hypothesis two-sided?Ha is not equal to146
13560027235What is a significance level?fixed value that we compare with the P-value, matter of judgement to determine if something is "statistically significant".147
13560027236What is the default significance level?α=.05148
13560027237Interpreting the p-valueif the true mean/proportion of the population is (null), the probability of getting a sample mean/proportion of _____ is (p-value).149
13560027238p value ≤ αWe reject our null hypothesis. There is sufficient evidence to say that (Ha) is true.150
13560027239p value ≥ αWe fail to reject our null hypothesis. There is insufficient evidence to say that (Ho) is not true.151
13560027240reject Ho when it is actually trueType I Error152
13560027241fail to reject Ho when it is actually falseType II Error153
13560027242Power definitionprobability of rejecting Ho when it is false154
13560027243probability of Type I Errorα155
13560027244probability of Type II Error1-power156
13560027245two ways to increase powerincrease sample size/significance level α157
135600272465 step process: z/t testState --> 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 Ho158
13560027282Formula for test statistic (μ)159
13560027247Formula for test statistic (p̂) (where p represents the null)(p̂-p)/(√((p)(1-p))/n)160
13560027248probability of a Type II Error?overlap normal distribution for null and true. Find rejection line. Use normalcdf161
13560027249when do you use z tests?for proportions162
13560027250when do you use t tests?for mean (population standard deviation unknown)163
13560027251finding p value for t teststcdf(min, max, df)164
13560027252Sample paired t teststate--> 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 conclusion165
13560027253What does statistically significant mean in context of a problem?The sample mean/proportion is far enough away from the true mean/proportion that it couldn't have happened by chance166
13560027254When doing a paired t-test, to check normality, what do you do?check the differences histogram (μ1-μ2)167
13560027255How to interpret a C% Confidence LevelIn C% of all possible samples of size n, we will construct an interval that captures the true parameter (in context).168
13560027256How to interpret a C% Confidence IntervalWe are C% confident that the interval (_,_) will capture the true parameter (in context).169
13560027257What conditions must be checked before constructing a confidence interval?random, normal, independent170
13560027258C% confidence intervals of sample proportions, 5 step processState: 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).171
13560027283What's the z interval standard error formula?172
13560027259How do you find z*?InvNorm(#)173
13560027260How do you find the point estimate of a sample?subtract the max and min confidence interval, divide it by two (aka find the mean of the interval ends)174
13560027261How do you find the margin of error, given the confidence interval?Ask, "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 ends175
13560027262Finding sample size proportions: When p hat is unknown, or you want to guarantee a margin of error less than or equal to:use p hat=.5176
13560027263Finding the confidence interval when the standard deviation of the population is *known*x bar +/- z*(σ/√n)177
13560027264Checking normal condition for z* (population standard deviation known)starts normal or CLT178
13560027265Finding the confidence interval when the standard deviation of the population is *unknown* (which is almost always true)x bar +/- t*(Sx/√n)179
13560027266degrees of freedomn-1180
13560027267How do you find t*?InvT(area to the left, df)181
13560027268What is the standard error?same as standard deviation, but we call it "standard error" because we plugged in p hat for p (we are estimating)182
13560027269a point estimator is a statistic that...provides an estimate of a population parameter.183
13560027270Explain the two conditions when the margin of error gets smaller.Confidence level C decreases, sample size n increases184
13560027271Does the confidence level tell us the chance that a particular confidence interval captures the population parameter?NO; the confidence interval gives us a set of plausible values for the parameter185
13560027272Sx and σx: which is which?Sx is for a sample, σx is for a population186
13560027273How do we know when do use a t* interval instead of a z interval?you are not given the population standard deviation187
13560027274Checking normal condition for t* (population standard deviation unknown)Normal for sample size... -n -n<15: if the data appears closely normal (roughly symmetric, single peak, no outliers)188
13560027275How to check if a distribution is normal for t*, population n<15plug data into List 1, look at histogram. Conclude with "The histogram looks roughly symmetric, so we should be safe to use the t distribution)189
13560027276t* confidence interval, 5 step processState: 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).190
13560027277margin of error formulaz* or t* (standard error)191
13560027278When calculating t interval, what is it and where do you find the data?x 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 given192
13560027279What is it looking for if it asks for the appropriate critical value?z/t* interval193
13560027284194

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