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AP Statistics Flashcards

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14605978560How do you check if there is outliers?calculate IQR; anything above Q3+1.5(IQR) or below Q1-1.5(IQR) is an outlier0
14605978561If a graph is skewed, should we calculate the median or the mean? Why?median; it is resistant to skews and outliers1
14605978562If 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
14605978563What is in the five number summary?Minimum, Q1, Median, Q3, Maximum3
14605978564Relationship between variance and standard deviation?variance=(standard deviation)^24
14605978565variance definitionthe variance is roughly the average of the squared differences between each observation and the mean5
14605978566standard deviationthe standard deviation is the square root of the variance6
14605978567What should we use to measure spread if the median was calculated?IQR7
14605978568What should we use to measure spread if the mean was calculated?standard deviation8
14605978569What is the IQR? How much of the data does it represent?Q3-Q1; 50%9
14605978570How 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
14605978750What is the formula for standard deviation?11
14605978571Categorical variables vs. Quantitative VariablesCategorical: individuals can be assigned to one of several groups or categories Quantitative: takes numberical values12
14605978572If a possible outlier is on the fence, is it an outlier?No13
14605978573Things 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
14605978574Explain 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
14605978575What 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
14605978576What is a density curve?a curve that (a) is on or above the horizontal axis, and (b) has exactly an area of 117
14605978577Inverse Normwhen you want to find the percentile: invNorm (area, mean, standard deviation)18
14605978578z(x-mean)/standard deviation19
14605978579pth percentilethe value with p percent observations less than is20
14605978580cumulative relative frequency graphcan be used to describe the position of an individual within a distribution or to locate a specified percentile of the distribution21
14605978581How 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
14605978582rtells us the strength of a LINEAR association. -1 to 1. Not resistant to outliers23
14605978583r^2the proportion (percent) of the variation in the values of y that can be accounted for by the least squares regression line24
14605978584residual 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
14605978585regression 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
14605978586residual formularesidual=y-y(hat) aka observed y - predicted y27
14605978587What 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
14605978588What 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
14605978589nnumber of trials30
14605978590pprobability of success31
14605978591knumber of successes32
14605978592Binomial Formula for P(X=k)(n choose k) p^k (1-p)^(n-k)33
14605978593Binomial Calculator Function to find P(X=k)binompdf(n,p,k)34
14605978594Binomial Calculator Function for P(X≤k)binomcdf(n,p,k)35
14605978595Binomial Calculator Function for P(X≥k)1-binomcdf(n,p,k-1)36
14605978596mean of a binomial distributionnp37
14605978597standard deviation of a binomial distribution√(np(1-p))38
14605978598Geometric Formula for P(X=k)(1-p)^(k-1) x p39
14605978599Geometric Calculator Function to find P(X=k)geometpdf(p,k)40
14605978600Geometric Calculator Function for P(X≤k)geometcdf(p,k)41
14605978601Geometric Calculator Function for P(X≥k)1-geometcdf(p,k-1)42
14605978602Mean of a geometric distribution1/p=expected number of trials until success43
14605978603Standard deviation of a geometric distribution√((1-p)/(p²))44
14605978604What 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
14605978605how do you enter n choose k into the calculator?type "n" on home screen, go to MATH --> PRB --> 3: ncr, type "k"46
14605978606μ(x+y)μx+μy47
14605978607μ(x-y)μx-μy48
14605978608σ(x+y)√(σ²x+σ²y)49
14605978609What 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
14605978610What 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
14605978611σ(x-y)√(σ²x+σ²y) --> you add to get the difference because variance is distance from mean and you cannot have a negative distance52
14605978612calculate μx by handX1P1+X2P2+.... XKPK (SigmaXKPK)53
14605978613calculate var(x) by hand(X1-μx)²p(1)+(X2-μx)²p(2)+.... (Sigma(Xk-μx)²p(k))54
14605978614Standard deviationsquare root of variance55
14605978615discrete random variablesa fixed set of possible x values (whole numbers)56
14605978616continuous 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
14605978617What 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
14605978618mutually exclusiveno outcomes in common59
14605978619addition rule for mutually exclusive events P (A U B)P(A)+P(B)60
14605978620complement rule P(A^C)1-P(A)61
14605978621general addition rule (not mutually exclusive) P(A U B)P(A)+P(B)-P(A n B)62
14605978622intersection P(A n B)both A and B will occur63
14605978623conditional probability P (A | B)P(A n B) / P(B)64
14605978624independent events (how to check independence)P(A) = P(A|B) P(B)= P(B|A)65
14605978625multiplication rule for independent events P(A n B)P(A) x P(B)66
14605978626general multiplication rule (non-independent events) P(A n B)P(A) x P(B|A)67
14605978627sample spacea list of possible outcomes68
14605978628probability modela description of some chance process that consists of 2 parts: a sample space S and a probability for each outcome69
14605978629eventany collection of outcomes from some chance process, designated by a capital letter (an event is a subset of the sample space)70
14605978630What 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
14605978631Complementprobability that an event does not occur72
14605978632What is the sum of the probabilities of all possible outcomes?173
14605978633What is the probability of two mutually exclusive events?P(A U B)= P(A)+P(B)74
14605978634five 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
14605978635When is a two-way table helpfuldisplays the sample space for probabilities involving two events more clearly76
14605978636In statistics, what is meant by the word "or"?could have either event or both77
14605978637When can a Venn Diagram be helpful?visually represents the probabilities of not mutually exclusive events78
14605978638What 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
14605978639What does the intersection of two or more events mean?both event A and event B occur80
14605978640What does the union of two or more events mean?either event A or event B (or both) occurs81
14605978641What 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
14605978642the 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
14605978643How do you interpret a probability?We interpret probability to represent the most accurate results if we did an infinite amount of trials84
14605978644What 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
14605978645simulationthe imitation of chance behavior, based on a model that accurately reflects the situation86
14605978646Name 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
14605978647What 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
14605978648What does the intersection of two or more events mean?both event A and event B occur89
14605978649sampleThe part of the population from which we actually collect information. We use information from a sample to draw conclusions about the entire population90
14605978650populationIn a statistical study, this is the entire group of individuals about which we want information91
14605978651sample 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
14605978652convenience sampleA sample selected by taking the members of the population that are easiest to reach; particularly prone to large bias.93
14605978653biasThe design of a statistical study shows ______ if it systematically favors certain outcomes.94
14605978654voluntary response samplePeople decide whether to join a sample based on an open invitation; particularly prone to large bias.95
14605978655random samplingThe use of chance to select a sample; is the central principle of statistical sampling.96
14605978656simple random sample (SRS)every set of n individuals has an equal chance to be the sample actually selected97
14605978657strataGroups of individuals in a population that are similar in some way that might affect their responses.98
14605978658stratified 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
14605978659cluster 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
14605978660inferenceDrawing conclusions that go beyond the data at hand.101
14605978661margin of errorTells how close the estimate tends to be to the unknown parameter in repeated random sampling.102
14605978662sampling frameThe list from which a sample is actually chosen.103
14605978663undercoverageOccurs when some members of the population are left out of the sampling frame; a type of sampling error.104
14605978664nonresponseOccurs when a selected individual cannot be contacted or refuses to cooperate; an example of a nonsampling error.105
14605978665wording 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
14605978666observational studyObserves individuals and measures variables of interest but does not attempt to influence the responses.107
14605978667experimentDeliberately imposes some treatment on individuals to measure their responses.108
14605978668explanatory variableA variable that helps explain or influences changes in a response variable.109
14605978669response variableA variable that measures an outcome of a study.110
14605978670lurking variablea variable that is not among the explanatory or response variables in a study but that may influence the response variable.111
14605978671treatmentA 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
14605978672experimental unitthe smallest collection of individuals to which treatments are applied.113
14605978673subjectsExperimental units that are human beings.114
14605978674factorsthe explanatory variables in an experiment are often called this115
14605978675random 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
14605978676replicationAn 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
14605978677double-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
14605978678single-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
14605978679placeboan inactive (fake) treatment120
14605978680placebo effectDescribes the fact that some subjects respond favorably to any treatment, even an inactive one121
14605978681blockA 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
14605978682inference 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
14605978683inference 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
14605978684lack 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
14605978685institutional 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
14605978686informed 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
14605978687simulationa model of random events128
14605978688censusa sample that includes the entire population129
14605978689population parametera number that measures a characteristic of a population130
14605978690systematic sampleevery fifth individual, for example, is chosen131
14605978691multistage samplea sampling design where several sampling methods are combined132
14605978692sampling variabilitythe naturally occurring variability found in samples133
14605978693levelsthe values that the experimenter used for a factor134
14605978694the four principles of experimental designcontrol, randomization, replication, and blocking135
14605978695completely randomized designa design where all experimental units have an equal chance of receiving any treatment136
14605978696interpreting p valueif the true mean/proportion of the population is (null), the probability of getting a sample mean/proportion of _____ is (p-value).137
14605978697p̂1-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
14605978698probability of getting a certain p̂1-p̂2 (ex. less than .1)plug in center and spread into bell curve, find probability139
14605978699Confidence intervals for difference in proportions formula(p̂1-p̂2) plus or minus z*(√((p1(1-p1)/n1)+(p2(1-p2)/n2))140
14605978700When do you use t and z test/intervals?t for mean z for proportions141
14605978751Significance test for difference in proportions142
14605978701What is a null hypothesis?What is being claimed. Statistical test designed to assess strength of evidence against null hypothesis. Abbreviated by Ho.143
14605978702What is an alternative hypothesis?the claim about the population that we are trying to find evidence FOR, abbreviated by Ha144
14605978703When is the alternative hypothesis one-sided?Ha less than or greater than145
14605978704When is the alternative hypothesis two-sided?Ha is not equal to146
14605978705What is a significance level?fixed value that we compare with the P-value, matter of judgement to determine if something is "statistically significant".147
14605978706What is the default significance level?α=.05148
14605978707Interpreting 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
14605978708p value ≤ αWe reject our null hypothesis. There is sufficient evidence to say that (Ha) is true.150
14605978709p value ≥ αWe fail to reject our null hypothesis. There is insufficient evidence to say that (Ho) is not true.151
14605978710reject Ho when it is actually trueType I Error152
14605978711fail to reject Ho when it is actually falseType II Error153
14605978712Power definitionprobability of rejecting Ho when it is false154
14605978713probability of Type I Errorα155
14605978714probability of Type II Error1-power156
14605978715two ways to increase powerincrease sample size/significance level α157
146059787165 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
14605978752Formula for test statistic (μ)159
14605978717Formula for test statistic (p̂) (where p represents the null)(p̂-p)/(√((p)(1-p))/n)160
14605978718probability of a Type II Error?overlap normal distribution for null and true. Find rejection line. Use normalcdf161
14605978719when do you use z tests?for proportions162
14605978720when do you use t tests?for mean (population standard deviation unknown)163
14605978721finding p value for t teststcdf(min, max, df)164
14605978722Sample 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
14605978723What 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
14605978724When doing a paired t-test, to check normality, what do you do?check the differences histogram (μ1-μ2)167
14605978725How 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
14605978726How to interpret a C% Confidence IntervalWe are C% confident that the interval (_,_) will capture the true parameter (in context).169
14605978727What conditions must be checked before constructing a confidence interval?random, normal, independent170
14605978728C% 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
14605978753What's the z interval standard error formula?172
14605978729How do you find z*?InvNorm(#)173
14605978730How 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
14605978731How 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
14605978732Finding 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
14605978733Finding the confidence interval when the standard deviation of the population is *known*x bar +/- z*(σ/√n)177
14605978734Checking normal condition for z* (population standard deviation known)starts normal or CLT178
14605978735Finding the confidence interval when the standard deviation of the population is *unknown* (which is almost always true)x bar +/- t*(Sx/√n)179
14605978736degrees of freedomn-1180
14605978737How do you find t*?InvT(area to the left, df)181
14605978738What 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
14605978739a point estimator is a statistic that...provides an estimate of a population parameter.183
14605978740Explain the two conditions when the margin of error gets smaller.Confidence level C decreases, sample size n increases184
14605978741Does 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
14605978742Sx and σx: which is which?Sx is for a sample, σx is for a population186
14605978743How do we know when do use a t* interval instead of a z interval?you are not given the population standard deviation187
14605978744Checking 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
14605978745How 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
14605978746t* 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
14605978747margin of error formulaz* or t* (standard error)191
14605978748When 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
14605978749What is it looking for if it asks for the appropriate critical value?z/t* interval193

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