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AP Statistics Flashcards

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14263261888How do you check if there is outliers?calculate IQR; anything above Q3+1.5(IQR) or below Q1-1.5(IQR) is an outlier0
14263261889If a graph is skewed, should we calculate the median or the mean? Why?median; it is resistant to skews and outliers1
14263261890If 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
14263261891What is in the five number summary?Minimum, Q1, Median, Q3, Maximum3
14263261892Relationship between variance and standard deviation?variance=(standard deviation)^24
14263261893variance definitionthe variance is roughly the average of the squared differences between each observation and the mean5
14263261894standard deviationthe standard deviation is the square root of the variance6
14263261895What should we use to measure spread if the median was calculated?IQR7
14263261896What should we use to measure spread if the mean was calculated?standard deviation8
14263261897What is the IQR? How much of the data does it represent?Q3-Q1; 50%9
14263261898How 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
14263262078What is the formula for standard deviation?11
14263261899Categorical variables vs. Quantitative VariablesCategorical: individuals can be assigned to one of several groups or categories Quantitative: takes numberical values12
14263261900If a possible outlier is on the fence, is it an outlier?No13
14263261901Things 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
14263261902Explain 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
14263261903What 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
14263261904What is a density curve?a curve that (a) is on or above the horizontal axis, and (b) has exactly an area of 117
14263261905Inverse Normwhen you want to find the percentile: invNorm (area, mean, standard deviation)18
14263261906z(x-mean)/standard deviation19
14263261907pth percentilethe value with p percent observations less than is20
14263261908cumulative relative frequency graphcan be used to describe the position of an individual within a distribution or to locate a specified percentile of the distribution21
14263261909How 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
14263261910rtells us the strength of a LINEAR association. -1 to 1. Not resistant to outliers23
14263261911r^2the proportion (percent) of the variation in the values of y that can be accounted for by the least squares regression line24
14263261912residual 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
14263261913regression 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
14263261914residual formularesidual=y-y(hat) aka observed y - predicted y27
14263261915What 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
14263261916What 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
14263261917nnumber of trials30
14263261918pprobability of success31
14263261919knumber of successes32
14263261920Binomial Formula for P(X=k)(n choose k) p^k (1-p)^(n-k)33
14263261921Binomial Calculator Function to find P(X=k)binompdf(n,p,k)34
14263261922Binomial Calculator Function for P(X≤k)binomcdf(n,p,k)35
14263261923Binomial Calculator Function for P(X≥k)1-binomcdf(n,p,k-1)36
14263261924mean of a binomial distributionnp37
14263261925standard deviation of a binomial distribution√(np(1-p))38
14263261926Geometric Formula for P(X=k)(1-p)^(k-1) x p39
14263261927Geometric Calculator Function to find P(X=k)geometpdf(p,k)40
14263261928Geometric Calculator Function for P(X≤k)geometcdf(p,k)41
14263261929Geometric Calculator Function for P(X≥k)1-geometcdf(p,k-1)42
14263261930Mean of a geometric distribution1/p=expected number of trials until success43
14263261931Standard deviation of a geometric distribution√((1-p)/(p²))44
14263261932What 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
14263261933how do you enter n choose k into the calculator?type "n" on home screen, go to MATH --> PRB --> 3: ncr, type "k"46
14263261934μ(x+y)μx+μy47
14263261935μ(x-y)μx-μy48
14263261936σ(x+y)√(σ²x+σ²y)49
14263261937What 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
14263261938What 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
14263261939σ(x-y)√(σ²x+σ²y) --> you add to get the difference because variance is distance from mean and you cannot have a negative distance52
14263261940calculate μx by handX1P1+X2P2+.... XKPK (SigmaXKPK)53
14263261941calculate var(x) by hand(X1-μx)²p(1)+(X2-μx)²p(2)+.... (Sigma(Xk-μx)²p(k))54
14263261942Standard deviationsquare root of variance55
14263261943discrete random variablesa fixed set of possible x values (whole numbers)56
14263261944continuous 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
14263261945What 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
14263261946mutually exclusiveno outcomes in common59
14263261947addition rule for mutually exclusive events P (A U B)P(A)+P(B)60
14263261948complement rule P(A^C)1-P(A)61
14263261949general addition rule (not mutually exclusive) P(A U B)P(A)+P(B)-P(A n B)62
14263261950intersection P(A n B)both A and B will occur63
14263261951conditional probability P (A | B)P(A n B) / P(B)64
14263261952independent events (how to check independence)P(A) = P(A|B) P(B)= P(B|A)65
14263261953multiplication rule for independent events P(A n B)P(A) x P(B)66
14263261954general multiplication rule (non-independent events) P(A n B)P(A) x P(B|A)67
14263261955sample spacea list of possible outcomes68
14263261956probability modela description of some chance process that consists of 2 parts: a sample space S and a probability for each outcome69
14263261957eventany collection of outcomes from some chance process, designated by a capital letter (an event is a subset of the sample space)70
14263261958What 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
14263261959Complementprobability that an event does not occur72
14263261960What is the sum of the probabilities of all possible outcomes?173
14263261961What is the probability of two mutually exclusive events?P(A U B)= P(A)+P(B)74
14263261962five 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
14263261963When is a two-way table helpfuldisplays the sample space for probabilities involving two events more clearly76
14263261964In statistics, what is meant by the word "or"?could have either event or both77
14263261965When can a Venn Diagram be helpful?visually represents the probabilities of not mutually exclusive events78
14263261966What 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
14263261967What does the intersection of two or more events mean?both event A and event B occur80
14263261968What does the union of two or more events mean?either event A or event B (or both) occurs81
14263261969What 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
14263261970the 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
14263261971How do you interpret a probability?We interpret probability to represent the most accurate results if we did an infinite amount of trials84
14263261972What 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
14263261973simulationthe imitation of chance behavior, based on a model that accurately reflects the situation86
14263261974Name 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
14263261975What 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
14263261976What does the intersection of two or more events mean?both event A and event B occur89
14263261977sampleThe part of the population from which we actually collect information. We use information from a sample to draw conclusions about the entire population90
14263261978populationIn a statistical study, this is the entire group of individuals about which we want information91
14263261979sample 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
14263261980convenience sampleA sample selected by taking the members of the population that are easiest to reach; particularly prone to large bias.93
14263261981biasThe design of a statistical study shows ______ if it systematically favors certain outcomes.94
14263261982voluntary response samplePeople decide whether to join a sample based on an open invitation; particularly prone to large bias.95
14263261983random samplingThe use of chance to select a sample; is the central principle of statistical sampling.96
14263261984simple random sample (SRS)every set of n individuals has an equal chance to be the sample actually selected97
14263261985strataGroups of individuals in a population that are similar in some way that might affect their responses.98
14263261986stratified 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
14263261987cluster 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
14263261988inferenceDrawing conclusions that go beyond the data at hand.101
14263261989margin of errorTells how close the estimate tends to be to the unknown parameter in repeated random sampling.102
14263261990sampling frameThe list from which a sample is actually chosen.103
14263261991undercoverageOccurs when some members of the population are left out of the sampling frame; a type of sampling error.104
14263261992nonresponseOccurs when a selected individual cannot be contacted or refuses to cooperate; an example of a nonsampling error.105
14263261993wording 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
14263261994observational studyObserves individuals and measures variables of interest but does not attempt to influence the responses.107
14263261995experimentDeliberately imposes some treatment on individuals to measure their responses.108
14263261996explanatory variableA variable that helps explain or influences changes in a response variable.109
14263261997response variableA variable that measures an outcome of a study.110
14263261998lurking variablea variable that is not among the explanatory or response variables in a study but that may influence the response variable.111
14263261999treatmentA 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
14263262000experimental unitthe smallest collection of individuals to which treatments are applied.113
14263262001subjectsExperimental units that are human beings.114
14263262002factorsthe explanatory variables in an experiment are often called this115
14263262003random 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
14263262004replicationAn 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
14263262005double-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
14263262006single-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
14263262007placeboan inactive (fake) treatment120
14263262008placebo effectDescribes the fact that some subjects respond favorably to any treatment, even an inactive one121
14263262009blockA 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
14263262010inference 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
14263262011inference 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
14263262012lack 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
14263262013institutional 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
14263262014informed 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
14263262015simulationa model of random events128
14263262016censusa sample that includes the entire population129
14263262017population parametera number that measures a characteristic of a population130
14263262018systematic sampleevery fifth individual, for example, is chosen131
14263262019multistage samplea sampling design where several sampling methods are combined132
14263262020sampling variabilitythe naturally occurring variability found in samples133
14263262021levelsthe values that the experimenter used for a factor134
14263262022the four principles of experimental designcontrol, randomization, replication, and blocking135
14263262023completely randomized designa design where all experimental units have an equal chance of receiving any treatment136
14263262024interpreting p valueif the true mean/proportion of the population is (null), the probability of getting a sample mean/proportion of _____ is (p-value).137
14263262025p̂1-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
14263262026probability of getting a certain p̂1-p̂2 (ex. less than .1)plug in center and spread into bell curve, find probability139
14263262027Confidence intervals for difference in proportions formula(p̂1-p̂2) plus or minus z*(√((p1(1-p1)/n1)+(p2(1-p2)/n2))140
14263262028When do you use t and z test/intervals?t for mean z for proportions141
14263262079Significance test for difference in proportions142
14263262029What is a null hypothesis?What is being claimed. Statistical test designed to assess strength of evidence against null hypothesis. Abbreviated by Ho.143
14263262030What is an alternative hypothesis?the claim about the population that we are trying to find evidence FOR, abbreviated by Ha144
14263262031When is the alternative hypothesis one-sided?Ha less than or greater than145
14263262032When is the alternative hypothesis two-sided?Ha is not equal to146
14263262033What is a significance level?fixed value that we compare with the P-value, matter of judgement to determine if something is "statistically significant".147
14263262034What is the default significance level?α=.05148
14263262035Interpreting 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
14263262036p value ≤ αWe reject our null hypothesis. There is sufficient evidence to say that (Ha) is true.150
14263262037p value ≥ αWe fail to reject our null hypothesis. There is insufficient evidence to say that (Ho) is not true.151
14263262038reject Ho when it is actually trueType I Error152
14263262039fail to reject Ho when it is actually falseType II Error153
14263262040Power definitionprobability of rejecting Ho when it is false154
14263262041probability of Type I Errorα155
14263262042probability of Type II Error1-power156
14263262043two ways to increase powerincrease sample size/significance level α157
142632620445 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
14263262080Formula for test statistic (μ)159
14263262045Formula for test statistic (p̂) (where p represents the null)(p̂-p)/(√((p)(1-p))/n)160
14263262046probability of a Type II Error?overlap normal distribution for null and true. Find rejection line. Use normalcdf161
14263262047when do you use z tests?for proportions162
14263262048when do you use t tests?for mean (population standard deviation unknown)163
14263262049finding p value for t teststcdf(min, max, df)164
14263262050Sample 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
14263262051What 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
14263262052When doing a paired t-test, to check normality, what do you do?check the differences histogram (μ1-μ2)167
14263262053How 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
14263262054How to interpret a C% Confidence IntervalWe are C% confident that the interval (_,_) will capture the true parameter (in context).169
14263262055What conditions must be checked before constructing a confidence interval?random, normal, independent170
14263262056C% 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
14263262081What's the z interval standard error formula?172
14263262057How do you find z*?InvNorm(#)173
14263262058How 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
14263262059How 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
14263262060Finding 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
14263262061Finding the confidence interval when the standard deviation of the population is *known*x bar +/- z*(σ/√n)177
14263262062Checking normal condition for z* (population standard deviation known)starts normal or CLT178
14263262063Finding the confidence interval when the standard deviation of the population is *unknown* (which is almost always true)x bar +/- t*(Sx/√n)179
14263262064degrees of freedomn-1180
14263262065How do you find t*?InvT(area to the left, df)181
14263262066What 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
14263262067a point estimator is a statistic that...provides an estimate of a population parameter.183
14263262068Explain the two conditions when the margin of error gets smaller.Confidence level C decreases, sample size n increases184
14263262069Does 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
14263262070Sx and σx: which is which?Sx is for a sample, σx is for a population186
14263262071How do we know when do use a t* interval instead of a z interval?you are not given the population standard deviation187
14263262072Checking 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
14263262073How 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
14263262074t* 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
14263262075margin of error formulaz* or t* (standard error)191
14263262076When 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
14263262077What is it looking for if it asks for the appropriate critical value?z/t* interval193

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