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AP Statistics Flashcards

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14010341899How do you check if there is outliers?calculate IQR; anything above Q3+1.5(IQR) or below Q1-1.5(IQR) is an outlier0
14010341900If a graph is skewed, should we calculate the median or the mean? Why?median; it is resistant to skews and outliers1
14010341901If 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
14010341902What is in the five number summary?Minimum, Q1, Median, Q3, Maximum3
14010341903Relationship between variance and standard deviation?variance=(standard deviation)^24
14010341904variance definitionthe variance is roughly the average of the squared differences between each observation and the mean5
14010341905standard deviationthe standard deviation is the square root of the variance6
14010341906What should we use to measure spread if the median was calculated?IQR7
14010341907What should we use to measure spread if the mean was calculated?standard deviation8
14010341908What is the IQR? How much of the data does it represent?Q3-Q1; 50%9
14010341909How 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
14010342089What is the formula for standard deviation?11
14010341910Categorical variables vs. Quantitative VariablesCategorical: individuals can be assigned to one of several groups or categories Quantitative: takes numberical values12
14010341911If a possible outlier is on the fence, is it an outlier?No13
14010341912Things 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
14010341913Explain 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
14010341914What 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
14010341915What is a density curve?a curve that (a) is on or above the horizontal axis, and (b) has exactly an area of 117
14010341916Inverse Normwhen you want to find the percentile: invNorm (area, mean, standard deviation)18
14010341917z(x-mean)/standard deviation19
14010341918pth percentilethe value with p percent observations less than is20
14010341919cumulative relative frequency graphcan be used to describe the position of an individual within a distribution or to locate a specified percentile of the distribution21
14010341920How 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
14010341921rtells us the strength of a LINEAR association. -1 to 1. Not resistant to outliers23
14010341922r^2the proportion (percent) of the variation in the values of y that can be accounted for by the least squares regression line24
14010341923residual 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
14010341924regression 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
14010341925residual formularesidual=y-y(hat) aka observed y - predicted y27
14010341926What 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
14010341927What 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
14010341928nnumber of trials30
14010341929pprobability of success31
14010341930knumber of successes32
14010341931Binomial Formula for P(X=k)(n choose k) p^k (1-p)^(n-k)33
14010341932Binomial Calculator Function to find P(X=k)binompdf(n,p,k)34
14010341933Binomial Calculator Function for P(X≤k)binomcdf(n,p,k)35
14010341934Binomial Calculator Function for P(X≥k)1-binomcdf(n,p,k-1)36
14010341935mean of a binomial distributionnp37
14010341936standard deviation of a binomial distribution√(np(1-p))38
14010341937Geometric Formula for P(X=k)(1-p)^(k-1) x p39
14010341938Geometric Calculator Function to find P(X=k)geometpdf(p,k)40
14010341939Geometric Calculator Function for P(X≤k)geometcdf(p,k)41
14010341940Geometric Calculator Function for P(X≥k)1-geometcdf(p,k-1)42
14010341941Mean of a geometric distribution1/p=expected number of trials until success43
14010341942Standard deviation of a geometric distribution√((1-p)/(p²))44
14010341943What 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
14010341944how do you enter n choose k into the calculator?type "n" on home screen, go to MATH --> PRB --> 3: ncr, type "k"46
14010341945μ(x+y)μx+μy47
14010341946μ(x-y)μx-μy48
14010341947σ(x+y)√(σ²x+σ²y)49
14010341948What 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
14010341949What 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
14010341950σ(x-y)√(σ²x+σ²y) --> you add to get the difference because variance is distance from mean and you cannot have a negative distance52
14010341951calculate μx by handX1P1+X2P2+.... XKPK (SigmaXKPK)53
14010341952calculate var(x) by hand(X1-μx)²p(1)+(X2-μx)²p(2)+.... (Sigma(Xk-μx)²p(k))54
14010341953Standard deviationsquare root of variance55
14010341954discrete random variablesa fixed set of possible x values (whole numbers)56
14010341955continuous 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
14010341956What 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
14010341957mutually exclusiveno outcomes in common59
14010341958addition rule for mutually exclusive events P (A U B)P(A)+P(B)60
14010341959complement rule P(A^C)1-P(A)61
14010341960general addition rule (not mutually exclusive) P(A U B)P(A)+P(B)-P(A n B)62
14010341961intersection P(A n B)both A and B will occur63
14010341962conditional probability P (A | B)P(A n B) / P(B)64
14010341963independent events (how to check independence)P(A) = P(A|B) P(B)= P(B|A)65
14010341964multiplication rule for independent events P(A n B)P(A) x P(B)66
14010341965general multiplication rule (non-independent events) P(A n B)P(A) x P(B|A)67
14010341966sample spacea list of possible outcomes68
14010341967probability modela description of some chance process that consists of 2 parts: a sample space S and a probability for each outcome69
14010341968eventany collection of outcomes from some chance process, designated by a capital letter (an event is a subset of the sample space)70
14010341969What 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
14010341970Complementprobability that an event does not occur72
14010341971What is the sum of the probabilities of all possible outcomes?173
14010341972What is the probability of two mutually exclusive events?P(A U B)= P(A)+P(B)74
14010341973five 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
14010341974When is a two-way table helpfuldisplays the sample space for probabilities involving two events more clearly76
14010341975In statistics, what is meant by the word "or"?could have either event or both77
14010341976When can a Venn Diagram be helpful?visually represents the probabilities of not mutually exclusive events78
14010341977What 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
14010341978What does the intersection of two or more events mean?both event A and event B occur80
14010341979What does the union of two or more events mean?either event A or event B (or both) occurs81
14010341980What 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
14010341981the 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
14010341982How do you interpret a probability?We interpret probability to represent the most accurate results if we did an infinite amount of trials84
14010341983What 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
14010341984simulationthe imitation of chance behavior, based on a model that accurately reflects the situation86
14010341985Name 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
14010341986What 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
14010341987What does the intersection of two or more events mean?both event A and event B occur89
14010341988sampleThe part of the population from which we actually collect information. We use information from a sample to draw conclusions about the entire population90
14010341989populationIn a statistical study, this is the entire group of individuals about which we want information91
14010341990sample 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
14010341991convenience sampleA sample selected by taking the members of the population that are easiest to reach; particularly prone to large bias.93
14010341992biasThe design of a statistical study shows ______ if it systematically favors certain outcomes.94
14010341993voluntary response samplePeople decide whether to join a sample based on an open invitation; particularly prone to large bias.95
14010341994random samplingThe use of chance to select a sample; is the central principle of statistical sampling.96
14010341995simple random sample (SRS)every set of n individuals has an equal chance to be the sample actually selected97
14010341996strataGroups of individuals in a population that are similar in some way that might affect their responses.98
14010341997stratified 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
14010341998cluster 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
14010341999inferenceDrawing conclusions that go beyond the data at hand.101
14010342000margin of errorTells how close the estimate tends to be to the unknown parameter in repeated random sampling.102
14010342001sampling frameThe list from which a sample is actually chosen.103
14010342002undercoverageOccurs when some members of the population are left out of the sampling frame; a type of sampling error.104
14010342003nonresponseOccurs when a selected individual cannot be contacted or refuses to cooperate; an example of a nonsampling error.105
14010342004wording 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
14010342005observational studyObserves individuals and measures variables of interest but does not attempt to influence the responses.107
14010342006experimentDeliberately imposes some treatment on individuals to measure their responses.108
14010342007explanatory variableA variable that helps explain or influences changes in a response variable.109
14010342008response variableA variable that measures an outcome of a study.110
14010342009lurking variablea variable that is not among the explanatory or response variables in a study but that may influence the response variable.111
14010342010treatmentA 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
14010342011experimental unitthe smallest collection of individuals to which treatments are applied.113
14010342012subjectsExperimental units that are human beings.114
14010342013factorsthe explanatory variables in an experiment are often called this115
14010342014random 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
14010342015replicationAn 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
14010342016double-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
14010342017single-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
14010342018placeboan inactive (fake) treatment120
14010342019placebo effectDescribes the fact that some subjects respond favorably to any treatment, even an inactive one121
14010342020blockA 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
14010342021inference 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
14010342022inference 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
14010342023lack 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
14010342024institutional 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
14010342025informed 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
14010342026simulationa model of random events128
14010342027censusa sample that includes the entire population129
14010342028population parametera number that measures a characteristic of a population130
14010342029systematic sampleevery fifth individual, for example, is chosen131
14010342030multistage samplea sampling design where several sampling methods are combined132
14010342031sampling variabilitythe naturally occurring variability found in samples133
14010342032levelsthe values that the experimenter used for a factor134
14010342033the four principles of experimental designcontrol, randomization, replication, and blocking135
14010342034completely randomized designa design where all experimental units have an equal chance of receiving any treatment136
14010342035interpreting p valueif the true mean/proportion of the population is (null), the probability of getting a sample mean/proportion of _____ is (p-value).137
14010342036p̂1-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
14010342037probability of getting a certain p̂1-p̂2 (ex. less than .1)plug in center and spread into bell curve, find probability139
14010342038Confidence intervals for difference in proportions formula(p̂1-p̂2) plus or minus z*(√((p1(1-p1)/n1)+(p2(1-p2)/n2))140
14010342039When do you use t and z test/intervals?t for mean z for proportions141
14010342090Significance test for difference in proportions142
14010342040What is a null hypothesis?What is being claimed. Statistical test designed to assess strength of evidence against null hypothesis. Abbreviated by Ho.143
14010342041What is an alternative hypothesis?the claim about the population that we are trying to find evidence FOR, abbreviated by Ha144
14010342042When is the alternative hypothesis one-sided?Ha less than or greater than145
14010342043When is the alternative hypothesis two-sided?Ha is not equal to146
14010342044What is a significance level?fixed value that we compare with the P-value, matter of judgement to determine if something is "statistically significant".147
14010342045What is the default significance level?α=.05148
14010342046Interpreting 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
14010342047p value ≤ αWe reject our null hypothesis. There is sufficient evidence to say that (Ha) is true.150
14010342048p value ≥ αWe fail to reject our null hypothesis. There is insufficient evidence to say that (Ho) is not true.151
14010342049reject Ho when it is actually trueType I Error152
14010342050fail to reject Ho when it is actually falseType II Error153
14010342051Power definitionprobability of rejecting Ho when it is false154
14010342052probability of Type I Errorα155
14010342053probability of Type II Error1-power156
14010342054two ways to increase powerincrease sample size/significance level α157
140103420555 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
14010342091Formula for test statistic (μ)159
14010342056Formula for test statistic (p̂) (where p represents the null)(p̂-p)/(√((p)(1-p))/n)160
14010342057probability of a Type II Error?overlap normal distribution for null and true. Find rejection line. Use normalcdf161
14010342058when do you use z tests?for proportions162
14010342059when do you use t tests?for mean (population standard deviation unknown)163
14010342060finding p value for t teststcdf(min, max, df)164
14010342061Sample 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
14010342062What 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
14010342063When doing a paired t-test, to check normality, what do you do?check the differences histogram (μ1-μ2)167
14010342064How 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
14010342065How to interpret a C% Confidence IntervalWe are C% confident that the interval (_,_) will capture the true parameter (in context).169
14010342066What conditions must be checked before constructing a confidence interval?random, normal, independent170
14010342067C% 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
14010342092What's the z interval standard error formula?172
14010342068How do you find z*?InvNorm(#)173
14010342069How 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
14010342070How 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
14010342071Finding 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
14010342072Finding the confidence interval when the standard deviation of the population is *known*x bar +/- z*(σ/√n)177
14010342073Checking normal condition for z* (population standard deviation known)starts normal or CLT178
14010342074Finding the confidence interval when the standard deviation of the population is *unknown* (which is almost always true)x bar +/- t*(Sx/√n)179
14010342075degrees of freedomn-1180
14010342076How do you find t*?InvT(area to the left, df)181
14010342077What 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
14010342078a point estimator is a statistic that...provides an estimate of a population parameter.183
14010342079Explain the two conditions when the margin of error gets smaller.Confidence level C decreases, sample size n increases184
14010342080Does 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
14010342081Sx and σx: which is which?Sx is for a sample, σx is for a population186
14010342082How do we know when do use a t* interval instead of a z interval?you are not given the population standard deviation187
14010342083Checking 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
14010342084How 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
14010342085t* 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
14010342086margin of error formulaz* or t* (standard error)191
14010342087When 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
14010342088What is it looking for if it asks for the appropriate critical value?z/t* interval193
14010342093194

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