AP Notes, Outlines, Study Guides, Vocabulary, Practice Exams and more!

AP Statistics (Set 2) Flashcards

Terms : Hide Images
9391390901How do you check if there is outliers?calculate IQR; anything above Q3+1.5(IQR) or below Q1-1.5(IQR) is an outlier0
9391390902If a graph is skewed, should we calculate the median or the mean? Why?median; it is resistant to skews and outliers1
9391390903If 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
9391390904What is in the five number summary?Minimum, Q1, Median, Q3, Maximum3
9391390905Relationship between variance and standard deviation?variance=(standard deviation)^24
9391390906variance definitionthe variance is roughly the average of the squared differences between each observation and the mean5
9391390907standard deviationthe standard deviation is the square root of the variance6
9391390908What should we use to measure spread if the median was calculated?IQR7
9391390909What should we use to measure spread if the mean was calculated?standard deviation8
9391390910What is the IQR? How much of the data does it represent?Q3-Q1; 50%9
9391390911How 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
9391391092What is the formula for standard deviation?11
9391390912Categorical variables vs. Quantitative VariablesCategorical: individuals can be assigned to one of several groups or categories Quantitative: takes numberical values12
9391390913If a possible outlier is on the fence, is it an outlier?No13
9391390914Things 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
9391390915Explain 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
9391390916What 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
9391390917What is a density curve?a curve that (a) is on or above the horizontal axis, and (b) has exactly an area of 117
9391390918Inverse Normwhen you want to find the percentile: invNorm (area, mean, standard deviation)18
9391390919z(x-mean)/standard deviation19
9391390920pth percentilethe value with p percent observations less than is20
9391390921cumulative relative frequency graphcan be used to describe the position of an individual within a distribution or to locate a specified percentile of the distribution21
9391390922How 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
9391390923rtells us the strength of a LINEAR association. -1 to 1. Not resistant to outliers23
9391390924r^2the proportion (percent) of the variation in the values of y that can be accounted for by the least squares regression line24
9391390925residual 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
9391390926regression 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
9391390927residual formularesidual=y-y(hat) aka observed y - predicted y27
9391390928What 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
9391390929What 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
9391390930nnumber of trials30
9391390931pprobability of success31
9391390932knumber of successes32
9391390933Binomial Formula for P(X=k)(n choose k) p^k (1-p)^(n-k)33
9391390934Binomial Calculator Function to find P(X=k)binompdf(n,p,k)34
9391390935Binomial Calculator Function for P(X≤k)binomcdf(n,p,k)35
9391390936Binomial Calculator Function for P(X≥k)1-binomcdf(n,p,k-1)36
9391390937mean of a binomial distributionnp37
9391390938standard deviation of a binomial distribution√(np(1-p))38
9391390939Geometric Formula for P(X=k)(1-p)^(k-1) x p39
9391390940Geometric Calculator Function to find P(X=k)geometpdf(p,k)40
9391390941Geometric Calculator Function for P(X≤k)geometcdf(p,k)41
9391390942Geometric Calculator Function for P(X≥k)1-geometcdf(p,k-1)42
9391390943Mean of a geometric distribution1/p=expected number of trials until success43
9391390944Standard deviation of a geometric distribution√((1-p)/(p²))44
9391390945What 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
9391390946how do you enter n choose k into the calculator?type "n" on home screen, go to MATH --> PRB --> 3: ncr, type "k"46
9391390947μ(x+y)μx+μy47
9391390948μ(x-y)μx-μy48
9391390949σ(x+y)√(σ²x+σ²y)49
9391390950What 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
9391390951What 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
9391390952σ(x-y)√(σ²x+σ²y) --> you add to get the difference because variance is distance from mean and you cannot have a negative distance52
9391390953calculate μx by handX1P1+X2P2+.... XKPK (SigmaXKPK)53
9391390954calculate var(x) by hand(X1-μx)²p(1)+(X2-μx)²p(2)+.... (Sigma(Xk-μx)²p(k))54
9391390955Standard deviationsquare root of variance55
9391390956discrete random variablesa fixed set of possible x values (whole numbers)56
9391390957continuous 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
9391390958What 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
9391390959mutually exclusiveno outcomes in common59
9391390960addition rule for mutually exclusive events P (A U B)P(A)+P(B)60
9391390961complement rule P(A^C)1-P(A)61
9391390962general addition rule (not mutually exclusive) P(A U B)P(A)+P(B)-P(A n B)62
9391390963intersection P(A n B)both A and B will occur63
9391390964conditional probability P (A | B)P(A n B) / P(B)64
9391390965independent events (how to check independence)P(A) = P(A|B) P(B)= P(B|A)65
9391390966multiplication rule for independent events P(A n B)P(A) x P(B)66
9391390967general multiplication rule (non-independent events) P(A n B)P(A) x P(B|A)67
9391390968sample spacea list of possible outcomes68
9391390969probability modela description of some chance process that consists of 2 parts: a sample space S and a probability for each outcome69
9391390970eventany collection of outcomes from some chance process, designated by a capital letter (an event is a subset of the sample space)70
9391390971What 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
9391390972Complementprobability that an event does not occur72
9391390973What is the sum of the probabilities of all possible outcomes?173
9391390974What is the probability of two mutually exclusive events?P(A U B)= P(A)+P(B)74
9391390975five 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
9391390976When is a two-way table helpfuldisplays the sample space for probabilities involving two events more clearly76
9391390977In statistics, what is meant by the word "or"?could have either event or both77
9391390978When can a Venn Diagram be helpful?visually represents the probabilities of not mutually exclusive events78
9391390979What 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
9391390980What does the intersection of two or more events mean?both event A and event B occur80
9391390981What does the union of two or more events mean?either event A or event B (or both) occurs81
9391390982What 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
9391390983the 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
9391390984How do you interpret a probability?We interpret probability to represent the most accurate results if we did an infinite amount of trials84
9391390985What 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
9391390986simulationthe imitation of chance behavior, based on a model that accurately reflects the situation86
9391390987Name 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
9391390988What 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
9391390989What does the intersection of two or more events mean?both event A and event B occur89
9391390990sampleThe part of the population from which we actually collect information. We use information from a sample to draw conclusions about the entire population90
9391390991populationIn a statistical study, this is the entire group of individuals about which we want information91
9391390992sample 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
9391390993convenience sampleA sample selected by taking the members of the population that are easiest to reach; particularly prone to large bias.93
9391390994biasThe design of a statistical study shows ______ if it systematically favors certain outcomes.94
9391390995voluntary response samplePeople decide whether to join a sample based on an open invitation; particularly prone to large bias.95
9391390996random samplingThe use of chance to select a sample; is the central principle of statistical sampling.96
9391390997simple random sample (SRS)every set of n individuals has an equal chance to be the sample actually selected97
9391390998strataGroups of individuals in a population that are similar in some way that might affect their responses.98
9391390999stratified 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
9391391000cluster 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
9391391001inferenceDrawing conclusions that go beyond the data at hand.101
9391391002margin of errorTells how close the estimate tends to be to the unknown parameter in repeated random sampling.102
9391391003sampling frameThe list from which a sample is actually chosen.103
9391391004undercoverageOccurs when some members of the population are left out of the sampling frame; a type of sampling error.104
9391391005nonresponseOccurs when a selected individual cannot be contacted or refuses to cooperate; an example of a nonsampling error.105
9391391006wording 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
9391391007observational studyObserves individuals and measures variables of interest but does not attempt to influence the responses.107
9391391008experimentDeliberately imposes some treatment on individuals to measure their responses.108
9391391009explanatory variableA variable that helps explain or influences changes in a response variable.109
9391391010response variableA variable that measures an outcome of a study.110
9391391011lurking variablea variable that is not among the explanatory or response variables in a study but that may influence the response variable.111
9391391012treatmentA 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
9391391013experimental unitthe smallest collection of individuals to which treatments are applied.113
9391391014subjectsExperimental units that are human beings.114
9391391015factorsthe explanatory variables in an experiment are often called this115
9391391016random 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
9391391017replicationAn 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
9391391018double-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
9391391019single-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
9391391020placeboan inactive (fake) treatment120
9391391021placebo effectDescribes the fact that some subjects respond favorably to any treatment, even an inactive one121
9391391022blockA 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
9391391023inference 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
9391391024inference 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
9391391025lack 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
9391391026institutional 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
9391391027informed 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
9391391028simulationa model of random events128
9391391029censusa sample that includes the entire population129
9391391030population parametera number that measures a characteristic of a population130
9391391031systematic sampleevery fifth individual, for example, is chosen131
9391391032multistage samplea sampling design where several sampling methods are combined132
9391391033sampling variabilitythe naturally occurring variability found in samples133
9391391034levelsthe values that the experimenter used for a factor134
9391391035the four principles of experimental designcontrol, randomization, replication, and blocking135
9391391036completely randomized designa design where all experimental units have an equal chance of receiving any treatment136
9391391037interpreting p valueif the true mean/proportion of the population is (null), the probability of getting a sample mean/proportion of _____ is (p-value).137
9391391038p̂1-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
9391391039probability of getting a certain p̂1-p̂2 (ex. less than .1)plug in center and spread into bell curve, find probability139
9391391040Confidence intervals for difference in proportions formula(p̂1-p̂2) plus or minus z*(√((p1(1-p1)/n1)+(p2(1-p2)/n2))140
9391391041When do you use t and z test/intervals?t for mean z for proportions141
9391391093Significance test for difference in proportions142
9391391042What is a null hypothesis?What is being claimed. Statistical test designed to assess strength of evidence against null hypothesis. Abbreviated by Ho.143
9391391043What is an alternative hypothesis?the claim about the population that we are trying to find evidence FOR, abbreviated by Ha144
9391391044When is the alternative hypothesis one-sided?Ha less than or greater than145
9391391045When is the alternative hypothesis two-sided?Ha is not equal to146
9391391046What is a significance level?fixed value that we compare with the P-value, matter of judgement to determine if something is "statistically significant".147
9391391047What is the default significance level?α=.05148
9391391048Interpreting 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
9391391049p value ≤ αWe reject our null hypothesis. There is sufficient evidence to say that (Ha) is true.150
9391391050p value ≥ αWe fail to reject our null hypothesis. There is insufficient evidence to say that (Ho) is not true.151
9391391051reject Ho when it is actually trueType I Error152
9391391052fail to reject Ho when it is actually falseType II Error153
9391391053Power definitionprobability of rejecting Ho when it is false154
9391391054probability of Type I Errorα155
9391391055probability of Type II Error1-power156
9391391056two ways to increase powerincrease sample size/significance level α157
93913910575 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
9391391094Formula for test statistic (μ)159
9391391058Formula for test statistic (p̂) (where p represents the null)(p̂-p)/(√((p)(1-p))/n)160
9391391059probability of a Type II Error?overlap normal distribution for null and true. Find rejection line. Use normalcdf161
9391391060when do you use z tests?for proportions162
9391391061when do you use t tests?for mean (population standard deviation unknown)163
9391391062finding p value for t teststcdf(min, max, df)164
9391391063Sample 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
9391391064What 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
9391391065When doing a paired t-test, to check normality, what do you do?check the differences histogram (μ1-μ2)167
9391391066How 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
9391391067How to interpret a C% Confidence IntervalWe are C% confident that the interval (_,_) will capture the true parameter (in context).169
9391391068What conditions must be checked before constructing a confidence interval?random, normal, independent170
9391391069C% 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
9391391095What's the z interval standard error formula?172
9391391070How do you find z*?InvNorm(#)173
9391391071How 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
9391391072How 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
9391391073Finding 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
9391391074Finding the confidence interval when the standard deviation of the population is *known*x bar +/- z*(σ/√n)177
9391391075Checking normal condition for z* (population standard deviation known)starts normal or CLT178
9391391076Finding the confidence interval when the standard deviation of the population is *unknown* (which is almost always true)x bar +/- t*(Sx/√n)179
9391391077degrees of freedomn-1180
9391391078How do you find t*?InvT(area to the left, df)181
9391391079What 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
9391391080a point estimator is a statistic that...provides an estimate of a population parameter.183
9391391081Explain the two conditions when the margin of error gets smaller.Confidence level C decreases, sample size n increases184
9391391082Does 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
9391391083Sx and σx: which is which?Sx is for a sample, σx is for a population186
9391391084How do we know when do use a t* interval instead of a z interval?you are not given the population standard deviation187
9391391085Checking 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
9391391086How 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
9391391087t* 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
9391391088margin of error formulaz* or t* (standard error)191
9391391089When 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
9391391090What is it looking for if it asks for the appropriate critical value?z/t* interval193

Need Help?

We hope your visit has been a productive one. If you're having any problems, or would like to give some feedback, we'd love to hear from you.

For general help, questions, and suggestions, try our dedicated support forums.

If you need to contact the Course-Notes.Org web experience team, please use our contact form.

Need Notes?

While we strive to provide the most comprehensive notes for as many high school textbooks as possible, there are certainly going to be some that we miss. Drop us a note and let us know which textbooks you need. Be sure to include which edition of the textbook you are using! If we see enough demand, we'll do whatever we can to get those notes up on the site for you!