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AP Statistics Flashcards

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13861182562How do you check if there is outliers?calculate IQR; anything above Q3+1.5(IQR) or below Q1-1.5(IQR) is an outlier0
13861182563If a graph is skewed, should we calculate the median or the mean? Why?median; it is resistant to skews and outliers1
13861182564If 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
13861182565What is in the five number summary?Minimum, Q1, Median, Q3, Maximum3
13861182566Relationship between variance and standard deviation?variance=(standard deviation)^24
13861182567variance definitionthe variance is roughly the average of the squared differences between each observation and the mean5
13861182568standard deviationthe standard deviation is the square root of the variance6
13861182569What should we use to measure spread if the median was calculated?IQR7
13861182570What should we use to measure spread if the mean was calculated?standard deviation8
13861182571What is the IQR? How much of the data does it represent?Q3-Q1; 50%9
13861182572How 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
13861182753What is the formula for standard deviation?11
13861182573Categorical variables vs. Quantitative VariablesCategorical: individuals can be assigned to one of several groups or categories Quantitative: takes numberical values12
13861182574If a possible outlier is on the fence, is it an outlier?No13
13861182575Things 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
13861182576Explain 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
13861182577What 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
13861182578What is a density curve?a curve that (a) is on or above the horizontal axis, and (b) has exactly an area of 117
13861182579Inverse Normwhen you want to find the percentile: invNorm (area, mean, standard deviation)18
13861182580z(x-mean)/standard deviation19
13861182581pth percentilethe value with p percent observations less than is20
13861182582cumulative relative frequency graphcan be used to describe the position of an individual within a distribution or to locate a specified percentile of the distribution21
13861182583How 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
13861182584rtells us the strength of a LINEAR association. -1 to 1. Not resistant to outliers23
13861182585r^2the proportion (percent) of the variation in the values of y that can be accounted for by the least squares regression line24
13861182586residual 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
13861182587regression 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
13861182588residual formularesidual=y-y(hat) aka observed y - predicted y27
13861182589What 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
13861182590What 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
13861182591nnumber of trials30
13861182592pprobability of success31
13861182593knumber of successes32
13861182594Binomial Formula for P(X=k)(n choose k) p^k (1-p)^(n-k)33
13861182595Binomial Calculator Function to find P(X=k)binompdf(n,p,k)34
13861182596Binomial Calculator Function for P(X≤k)binomcdf(n,p,k)35
13861182597Binomial Calculator Function for P(X≥k)1-binomcdf(n,p,k-1)36
13861182598mean of a binomial distributionnp37
13861182599standard deviation of a binomial distribution√(np(1-p))38
13861182600Geometric Formula for P(X=k)(1-p)^(k-1) x p39
13861182601Geometric Calculator Function to find P(X=k)geometpdf(p,k)40
13861182602Geometric Calculator Function for P(X≤k)geometcdf(p,k)41
13861182603Geometric Calculator Function for P(X≥k)1-geometcdf(p,k-1)42
13861182604Mean of a geometric distribution1/p=expected number of trials until success43
13861182605Standard deviation of a geometric distribution√((1-p)/(p²))44
13861182606What 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
13861182607how do you enter n choose k into the calculator?type "n" on home screen, go to MATH --> PRB --> 3: ncr, type "k"46
13861182608μ(x+y)μx+μy47
13861182609μ(x-y)μx-μy48
13861182610σ(x+y)√(σ²x+σ²y)49
13861182611What 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
13861182612What 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
13861182613σ(x-y)√(σ²x+σ²y) --> you add to get the difference because variance is distance from mean and you cannot have a negative distance52
13861182614calculate μx by handX1P1+X2P2+.... XKPK (SigmaXKPK)53
13861182615calculate var(x) by hand(X1-μx)²p(1)+(X2-μx)²p(2)+.... (Sigma(Xk-μx)²p(k))54
13861182616Standard deviationsquare root of variance55
13861182617discrete random variablesa fixed set of possible x values (whole numbers)56
13861182618continuous 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
13861182619What 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
13861182620mutually exclusiveno outcomes in common59
13861182621addition rule for mutually exclusive events P (A U B)P(A)+P(B)60
13861182622complement rule P(A^C)1-P(A)61
13861182623general addition rule (not mutually exclusive) P(A U B)P(A)+P(B)-P(A n B)62
13861182624intersection P(A n B)both A and B will occur63
13861182625conditional probability P (A | B)P(A n B) / P(B)64
13861182626independent events (how to check independence)P(A) = P(A|B) P(B)= P(B|A)65
13861182627multiplication rule for independent events P(A n B)P(A) x P(B)66
13861182628general multiplication rule (non-independent events) P(A n B)P(A) x P(B|A)67
13861182629sample spacea list of possible outcomes68
13861182630probability modela description of some chance process that consists of 2 parts: a sample space S and a probability for each outcome69
13861182631eventany collection of outcomes from some chance process, designated by a capital letter (an event is a subset of the sample space)70
13861182632What 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
13861182633Complementprobability that an event does not occur72
13861182634What is the sum of the probabilities of all possible outcomes?173
13861182635What is the probability of two mutually exclusive events?P(A U B)= P(A)+P(B)74
13861182636five 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
13861182637When is a two-way table helpfuldisplays the sample space for probabilities involving two events more clearly76
13861182638In statistics, what is meant by the word "or"?could have either event or both77
13861182639When can a Venn Diagram be helpful?visually represents the probabilities of not mutually exclusive events78
13861182640What 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
13861182641What does the intersection of two or more events mean?both event A and event B occur80
13861182642What does the union of two or more events mean?either event A or event B (or both) occurs81
13861182643What 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
13861182644the 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
13861182645How do you interpret a probability?We interpret probability to represent the most accurate results if we did an infinite amount of trials84
13861182646What 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
13861182647simulationthe imitation of chance behavior, based on a model that accurately reflects the situation86
13861182648Name 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
13861182649What 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
13861182650What does the intersection of two or more events mean?both event A and event B occur89
13861182651sampleThe part of the population from which we actually collect information. We use information from a sample to draw conclusions about the entire population90
13861182652populationIn a statistical study, this is the entire group of individuals about which we want information91
13861182653sample 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
13861182654convenience sampleA sample selected by taking the members of the population that are easiest to reach; particularly prone to large bias.93
13861182655biasThe design of a statistical study shows ______ if it systematically favors certain outcomes.94
13861182656voluntary response samplePeople decide whether to join a sample based on an open invitation; particularly prone to large bias.95
13861182657random samplingThe use of chance to select a sample; is the central principle of statistical sampling.96
13861182658simple random sample (SRS)every set of n individuals has an equal chance to be the sample actually selected97
13861182659strataGroups of individuals in a population that are similar in some way that might affect their responses.98
13861182660stratified 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
13861182661cluster 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
13861182662inferenceDrawing conclusions that go beyond the data at hand.101
13861182663margin of errorTells how close the estimate tends to be to the unknown parameter in repeated random sampling.102
13861182664sampling frameThe list from which a sample is actually chosen.103
13861182665undercoverageOccurs when some members of the population are left out of the sampling frame; a type of sampling error.104
13861182666nonresponseOccurs when a selected individual cannot be contacted or refuses to cooperate; an example of a nonsampling error.105
13861182667wording 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
13861182668observational studyObserves individuals and measures variables of interest but does not attempt to influence the responses.107
13861182669experimentDeliberately imposes some treatment on individuals to measure their responses.108
13861182670explanatory variableA variable that helps explain or influences changes in a response variable.109
13861182671response variableA variable that measures an outcome of a study.110
13861182672lurking variablea variable that is not among the explanatory or response variables in a study but that may influence the response variable.111
13861182673treatmentA 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
13861182674experimental unitthe smallest collection of individuals to which treatments are applied.113
13861182675subjectsExperimental units that are human beings.114
13861182676factorsthe explanatory variables in an experiment are often called this115
13861182677random 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
13861182678replicationAn 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
13861182679double-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
13861182680single-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
13861182681placeboan inactive (fake) treatment120
13861182682placebo effectDescribes the fact that some subjects respond favorably to any treatment, even an inactive one121
13861182683blockA 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
13861182684inference 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
13861182685inference 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
13861182686lack 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
13861182687institutional 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
13861182688informed 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
13861182689simulationa model of random events128
13861182690censusa sample that includes the entire population129
13861182691population parametera number that measures a characteristic of a population130
13861182692systematic sampleevery fifth individual, for example, is chosen131
13861182693multistage samplea sampling design where several sampling methods are combined132
13861182694sampling variabilitythe naturally occurring variability found in samples133
13861182695levelsthe values that the experimenter used for a factor134
13861182696the four principles of experimental designcontrol, randomization, replication, and blocking135
13861182697completely randomized designa design where all experimental units have an equal chance of receiving any treatment136
13861182698interpreting p valueif the true mean/proportion of the population is (null), the probability of getting a sample mean/proportion of _____ is (p-value).137
13861182699p̂1-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
13861182700probability of getting a certain p̂1-p̂2 (ex. less than .1)plug in center and spread into bell curve, find probability139
13861182701Confidence intervals for difference in proportions formula(p̂1-p̂2) plus or minus z*(√((p1(1-p1)/n1)+(p2(1-p2)/n2))140
13861182702When do you use t and z test/intervals?t for mean z for proportions141
13861182754Significance test for difference in proportions142
13861182703What is a null hypothesis?What is being claimed. Statistical test designed to assess strength of evidence against null hypothesis. Abbreviated by Ho.143
13861182704What is an alternative hypothesis?the claim about the population that we are trying to find evidence FOR, abbreviated by Ha144
13861182705When is the alternative hypothesis one-sided?Ha less than or greater than145
13861182706When is the alternative hypothesis two-sided?Ha is not equal to146
13861182707What is a significance level?fixed value that we compare with the P-value, matter of judgement to determine if something is "statistically significant".147
13861182708What is the default significance level?α=.05148
13861182709Interpreting 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
13861182710p value ≤ αWe reject our null hypothesis. There is sufficient evidence to say that (Ha) is true.150
13861182711p value ≥ αWe fail to reject our null hypothesis. There is insufficient evidence to say that (Ho) is not true.151
13861182712reject Ho when it is actually trueType I Error152
13861182713fail to reject Ho when it is actually falseType II Error153
13861182714Power definitionprobability of rejecting Ho when it is false154
13861182715probability of Type I Errorα155
13861182716probability of Type II Error1-power156
13861182717two ways to increase powerincrease sample size/significance level α157
138611827185 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
13861182755Formula for test statistic (μ)159
13861182719Formula for test statistic (p̂) (where p represents the null)(p̂-p)/(√((p)(1-p))/n)160
13861182720probability of a Type II Error?overlap normal distribution for null and true. Find rejection line. Use normalcdf161
13861182721when do you use z tests?for proportions162
13861182722when do you use t tests?for mean (population standard deviation unknown)163
13861182723finding p value for t teststcdf(min, max, df)164
13861182724Sample 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
13861182725What 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
13861182726When doing a paired t-test, to check normality, what do you do?check the differences histogram (μ1-μ2)167
13861182727How 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
13861182728How to interpret a C% Confidence IntervalWe are C% confident that the interval (_,_) will capture the true parameter (in context).169
13861182729What conditions must be checked before constructing a confidence interval?random, normal, independent170
13861182730C% 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
13861182756What's the z interval standard error formula?172
13861182731How do you find z*?InvNorm(#)173
13861182732How 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
13861182733How 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
13861182734Finding 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
13861182735Finding the confidence interval when the standard deviation of the population is *known*x bar +/- z*(σ/√n)177
13861182736Checking normal condition for z* (population standard deviation known)starts normal or CLT178
13861182737Finding the confidence interval when the standard deviation of the population is *unknown* (which is almost always true)x bar +/- t*(Sx/√n)179
13861182738degrees of freedomn-1180
13861182739How do you find t*?InvT(area to the left, df)181
13861182740What 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
13861182741a point estimator is a statistic that...provides an estimate of a population parameter.183
13861182742Explain the two conditions when the margin of error gets smaller.Confidence level C decreases, sample size n increases184
13861182743Does 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
13861182744Sx and σx: which is which?Sx is for a sample, σx is for a population186
13861182745How do we know when do use a t* interval instead of a z interval?you are not given the population standard deviation187
13861182746Checking 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
13861182747How 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
13861182748t* 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
13861182749margin of error formulaz* or t* (standard error)191
13861182750When 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
13861182751What is it looking for if it asks for the appropriate critical value?z/t* interval193

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