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AP Statistics Flashcards

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5949881878How do you check if there is outliers?calculate IQR; anything above Q3+1.5(IQR) or below Q1-1.5(IQR) is an outlier0
5949881879If a graph is skewed, should we calculate the median or the mean? Why?median; it is resistant to skews and outliers1
5949881880If 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
5949881881What is in the five number summary?Minimum, Q1, Median, Q3, Maximum3
5949881882Relationship between variance and standard deviation?variance=(standard deviation)^24
5949881883variance definitionthe variance is roughly the average of the squared differences between each observation and the mean5
5949881884standard deviationthe standard deviation is the square root of the variance6
5949881885What should we use to measure spread if the median was calculated?IQR7
5949881886What should we use to measure spread if the mean was calculated?standard deviation8
5949881887What is the IQR? How much of the data does it represent?Q3-Q1; 50%9
5949881888How 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
5949881889What is the formula for standard deviation?11
5949881890Categorical variables vs. Quantitative VariablesCategorical: individuals can be assigned to one of several groups or categories Quantitative: takes numberical values12
5949881891If a possible outlier is on the fence, is it an outlier?No13
5949881892Things 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
5949881893Explain 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
5949881894What 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
5949881895What is a density curve?a curve that (a) is on or above the horizontal axis, and (b) has exactly an area of 117
5949881896Inverse Normwhen you want to find the percentile: invNorm (area, mean, standard deviation)18
5949881897z(x-mean)/standard deviation19
5949881898pth percentilethe value with p percent observations less than is20
5949881899cumulative relative frequency graphcan be used to describe the position of an individual within a distribution or to locate a specified percentile of the distribution21
5949881900How 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
5949881901rtells us the strength of a LINEAR association. -1 to 1. Not resistant to outliers23
5949881902r^2the proportion (percent) of the variation in the values of y that can be accounted for by the least squares regression line24
5949881903residual 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
5949881904regression 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
5949881905residual formularesidual=y-y(hat) aka observed y - predicted y27
5949881906What 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
5949881907What 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
5949881908nnumber of trials30
5949881909pprobability of success31
5949881910knumber of successes32
5949881911Binomial Formula for P(X=k)(n choose k) p^k (1-p)^(n-k)33
5949881912Binomial Calculator Function to find P(X=k)binompdf(n,p,k)34
5949881913Binomial Calculator Function for P(X≤k)binomcdf(n,p,k)35
5949881914Binomial Calculator Function for P(X≥k)1-binomcdf(n,p,k-1)36
5949881915mean of a binomial distributionnp37
5949881916standard deviation of a binomial distribution√(np(1-p))38
5949881917Geometric Formula for P(X=k)(1-p)^(k-1) x p39
5949881918Geometric Calculator Function to find P(X=k)geometpdf(p,k)40
5949881919Geometric Calculator Function for P(X≤k)geometcdf(p,k)41
5949881920Geometric Calculator Function for P(X≥k)1-geometcdf(p,k-1)42
5949881921Mean of a geometric distribution1/p=expected number of trials until success43
5949881922Standard deviation of a geometric distribution√((1-p)/(p²))44
5949881923What 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
5949881924how do you enter n choose k into the calculator?type "n" on home screen, go to MATH --> PRB --> 3: ncr, type "k"46
5949881925μ(x+y)μx+μy47
5949881926μ(x-y)μx-μy48
5949881927σ(x+y)√(σ²x+σ²y)49
5949881928What 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
5949881929What 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
5949881930σ(x-y)√(σ²x+σ²y) --> you add to get the difference because variance is distance from mean and you cannot have a negative distance52
5949881931calculate μx by handX1P1+X2P2+.... XKPK (SigmaXKPK)53
5949881932calculate var(x) by hand(X1-μx)²p(1)+(X2-μx)²p(2)+.... (Sigma(Xk-μx)²p(k))54
5949881933Standard deviationsquare root of variance55
5949881934discrete random variablesa fixed set of possible x values (whole numbers)56
5949881935continuous 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
5949881936What 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
5949881937mutually exclusiveno outcomes in common59
5949881938addition rule for mutually exclusive events P (A U B)P(A)+P(B)60
5949881939complement rule P(A^C)1-P(A)61
5949881940general addition rule (not mutually exclusive) P(A U B)P(A)+P(B)-P(A n B)62
5949881941intersection P(A n B)both A and B will occur63
5949881942conditional probability P (A | B)P(A n B) / P(B)64
5949881943independent events (how to check independence)P(A) = P(A|B) P(B)= P(B|A)65
5949881944multiplication rule for independent events P(A n B)P(A) x P(B)66
5949881945general multiplication rule (non-independent events) P(A n B)P(A) x P(B|A)67
5949881946sample spacea list of possible outcomes68
5949881947probability modela description of some chance process that consists of 2 parts: a sample space S and a probability for each outcome69
5949881948eventany collection of outcomes from some chance process, designated by a capital letter (an event is a subset of the sample space)70
5949881949What 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
5949881950Complementprobability that an event does not occur72
5949881951What is the sum of the probabilities of all possible outcomes?173
5949881952What is the probability of two mutually exclusive events?P(A U B)= P(A)+P(B)74
5949881953five 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
5949881954When is a two-way table helpfuldisplays the sample space for probabilities involving two events more clearly76
5949881955In statistics, what is meant by the word "or"?could have either event or both77
5949881956When can a Venn Diagram be helpful?visually represents the probabilities of not mutually exclusive events78
5949881957What 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
5949881958What does the intersection of two or more events mean?both event A and event B occur80
5949881959What does the union of two or more events mean?either event A or event B (or both) occurs81
5949881960What 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
5949881961the 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
5949881962How do you interpret a probability?We interpret probability to represent the most accurate results if we did an infinite amount of trials84
5949881963What 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
5949881964simulationthe imitation of chance behavior, based on a model that accurately reflects the situation86
5949881965Name 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
5949881966What 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
5949881967What does the intersection of two or more events mean?both event A and event B occur89
5949881968sampleThe part of the population from which we actually collect information. We use information from a sample to draw conclusions about the entire population90
5949881969populationIn a statistical study, this is the entire group of individuals about which we want information91
5949881970sample 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
5949881971convenience sampleA sample selected by taking the members of the population that are easiest to reach; particularly prone to large bias.93
5949881972biasThe design of a statistical study shows ______ if it systematically favors certain outcomes.94
5949881973voluntary response samplePeople decide whether to join a sample based on an open invitation; particularly prone to large bias.95
5949881974random samplingThe use of chance to select a sample; is the central principle of statistical sampling.96
5949881975simple random sample (SRS)every set of n individuals has an equal chance to be the sample actually selected97
5949881976strataGroups of individuals in a population that are similar in some way that might affect their responses.98
5949881977stratified 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
5949881978cluster 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
5949881979inferenceDrawing conclusions that go beyond the data at hand.101
5949881980margin of errorTells how close the estimate tends to be to the unknown parameter in repeated random sampling.102
5949881981sampling frameThe list from which a sample is actually chosen.103
5949881982undercoverageOccurs when some members of the population are left out of the sampling frame; a type of sampling error.104
5949881983nonresponseOccurs when a selected individual cannot be contacted or refuses to cooperate; an example of a nonsampling error.105
5949881984wording 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
5949881985observational studyObserves individuals and measures variables of interest but does not attempt to influence the responses.107
5949881986experimentDeliberately imposes some treatment on individuals to measure their responses.108
5949881987explanatory variableA variable that helps explain or influences changes in a response variable.109
5949881988response variableA variable that measures an outcome of a study.110
5949881989lurking variablea variable that is not among the explanatory or response variables in a study but that may influence the response variable.111
5949881990treatmentA 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
5949881991experimental unitthe smallest collection of individuals to which treatments are applied.113
5949881992subjectsExperimental units that are human beings.114
5949881993factorsthe explanatory variables in an experiment are often called this115
5949881994random 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
5949881995replicationAn 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
5949881996double-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
5949881997single-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
5949881998placeboan inactive (fake) treatment120
5949881999placebo effectDescribes the fact that some subjects respond favorably to any treatment, even an inactive one121
5949882000blockA 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
5949882001inference 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
5949882002inference 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
5949882003lack 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
5949882004institutional 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
5949882005informed 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
5949882006simulationa model of random events128
5949882007censusa sample that includes the entire population129
5949882008population parametera number that measures a characteristic of a population130
5949882009systematic sampleevery fifth individual, for example, is chosen131
5949882010multistage samplea sampling design where several sampling methods are combined132
5949882011sampling variabilitythe naturally occurring variability found in samples133
5949882012levelsthe values that the experimenter used for a factor134
5949882013the four principles of experimental designcontrol, randomization, replication, and blocking135
5949882014completely randomized designa design where all experimental units have an equal chance of receiving any treatment136
5949882015interpreting p valueif the true mean/proportion of the population is (null), the probability of getting a sample mean/proportion of _____ is (p-value).137
5949882016p̂1-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
5949882017probability of getting a certain p̂1-p̂2 (ex. less than .1)plug in center and spread into bell curve, find probability139
5949882018Confidence intervals for difference in proportions formula(p̂1-p̂2) plus or minus z*(√((p1(1-p1)/n1)+(p2(1-p2)/n2))140
5949882019When do you use t and z test/intervals?t for mean z for proportions141
5949882020Significance test for difference in proportions142
5949882021What is a null hypothesis?What is being claimed. Statistical test designed to assess strength of evidence against null hypothesis. Abbreviated by Ho.143
5949882022What is an alternative hypothesis?the claim about the population that we are trying to find evidence FOR, abbreviated by Ha144
5949882023When is the alternative hypothesis one-sided?Ha less than or greater than145
5949882024When is the alternative hypothesis two-sided?Ha is not equal to146
5949882025What is a significance level?fixed value that we compare with the P-value, matter of judgement to determine if something is "statistically significant".147
5949882026What is the default significance level?α=.05148
5949882027Interpreting 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
5949882028p value ≤ αWe reject our null hypothesis. There is sufficient evidence to say that (Ha) is true.150
5949882029p value ≥ αWe fail to reject our null hypothesis. There is insufficient evidence to say that (Ho) is not true.151
5949882030reject Ho when it is actually trueType I Error152
5949882031fail to reject Ho when it is actually falseType II Error153
5949882032Power definitionprobability of rejecting Ho when it is false154
5949882033probability of Type I Errorα155
5949882034probability of Type II Error1-power156
5949882035two ways to increase powerincrease sample size/significance level α157
59498820365 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
5949882037Formula for test statistic (μ)159
5949882038Formula for test statistic (p̂) (where p represents the null)(p̂-p)/(√((p)(1-p))/n)160
5949882039probability of a Type II Error?overlap normal distribution for null and true. Find rejection line. Use normalcdf161
5949882040when do you use z tests?for proportions162
5949882041when do you use t tests?for mean (population standard deviation unknown)163
5949882042finding p value for t teststcdf(min, max, df)164
5949882043Sample 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
5949882044What 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
5949882045When doing a paired t-test, to check normality, what do you do?check the differences histogram (μ1-μ2)167
5949882046How 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
5949882047How to interpret a C% Confidence IntervalWe are C% confident that the interval (_,_) will capture the true parameter (in context).169
5949882048What conditions must be checked before constructing a confidence interval?random, normal, independent170
5949882049C% 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
5949882050What's the z interval standard error formula?172
5949882051How do you find z*?InvNorm(#)173
5949882052How 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
5949882053How 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
5949882054Finding 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
5949882055Finding the confidence interval when the standard deviation of the population is *known*x bar +/- z*(σ/√n)177
5949882056Checking normal condition for z* (population standard deviation known)starts normal or CLT178
5949882057Finding the confidence interval when the standard deviation of the population is *unknown* (which is almost always true)x bar +/- t*(Sx/√n)179
5949882058degrees of freedomn-1180
5949882059How do you find t*?InvT(area to the left, df)181
5949882060What 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
5949882061a point estimator is a statistic that...provides an estimate of a population parameter.183
5949882062Explain the two conditions when the margin of error gets smaller.Confidence level C decreases, sample size n increases184
5949882063Does 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
5949882064Sx and σx: which is which?Sx is for a sample, σx is for a population186
5949882065How do we know when do use a t* interval instead of a z interval?you are not given the population standard deviation187
5949882066Checking 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
5949882067How 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
5949882068t* 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
5949882069margin of error formulaz* or t* (standard error)191
5949882070When 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
5949882071What is it looking for if it asks for the appropriate critical value?z/t* interval193

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