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AP Statistics Flashcards

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14005811225How do you check if there is outliers?calculate IQR; anything above Q3+1.5(IQR) or below Q1-1.5(IQR) is an outlier0
14005811226If a graph is skewed, should we calculate the median or the mean? Why?median; it is resistant to skews and outliers1
14005811227If 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
14005811228What is in the five number summary?Minimum, Q1, Median, Q3, Maximum3
14005811229Relationship between variance and standard deviation?variance=(standard deviation)^24
14005811230variance definitionthe variance is roughly the average of the squared differences between each observation and the mean5
14005811231standard deviationthe standard deviation is the square root of the variance6
14005811232What should we use to measure spread if the median was calculated?IQR7
14005811233What should we use to measure spread if the mean was calculated?standard deviation8
14005811234What is the IQR? How much of the data does it represent?Q3-Q1; 50%9
14005811235How 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
14005811415What is the formula for standard deviation?11
14005811236Categorical variables vs. Quantitative VariablesCategorical: individuals can be assigned to one of several groups or categories Quantitative: takes numberical values12
14005811237If a possible outlier is on the fence, is it an outlier?No13
14005811238Things 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
14005811239Explain 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
14005811240What 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
14005811241What is a density curve?a curve that (a) is on or above the horizontal axis, and (b) has exactly an area of 117
14005811242Inverse Normwhen you want to find the percentile: invNorm (area, mean, standard deviation)18
14005811243z(x-mean)/standard deviation19
14005811244pth percentilethe value with p percent observations less than is20
14005811245cumulative relative frequency graphcan be used to describe the position of an individual within a distribution or to locate a specified percentile of the distribution21
14005811246How 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
14005811247rtells us the strength of a LINEAR association. -1 to 1. Not resistant to outliers23
14005811248r^2the proportion (percent) of the variation in the values of y that can be accounted for by the least squares regression line24
14005811249residual 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
14005811250regression 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
14005811251residual formularesidual=y-y(hat) aka observed y - predicted y27
14005811252What 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
14005811253What 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
14005811254nnumber of trials30
14005811255pprobability of success31
14005811256knumber of successes32
14005811257Binomial Formula for P(X=k)(n choose k) p^k (1-p)^(n-k)33
14005811258Binomial Calculator Function to find P(X=k)binompdf(n,p,k)34
14005811259Binomial Calculator Function for P(X≤k)binomcdf(n,p,k)35
14005811260Binomial Calculator Function for P(X≥k)1-binomcdf(n,p,k-1)36
14005811261mean of a binomial distributionnp37
14005811262standard deviation of a binomial distribution√(np(1-p))38
14005811263Geometric Formula for P(X=k)(1-p)^(k-1) x p39
14005811264Geometric Calculator Function to find P(X=k)geometpdf(p,k)40
14005811265Geometric Calculator Function for P(X≤k)geometcdf(p,k)41
14005811266Geometric Calculator Function for P(X≥k)1-geometcdf(p,k-1)42
14005811267Mean of a geometric distribution1/p=expected number of trials until success43
14005811268Standard deviation of a geometric distribution√((1-p)/(p²))44
14005811269What 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
14005811270how do you enter n choose k into the calculator?type "n" on home screen, go to MATH --> PRB --> 3: ncr, type "k"46
14005811271μ(x+y)μx+μy47
14005811272μ(x-y)μx-μy48
14005811273σ(x+y)√(σ²x+σ²y)49
14005811274What 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
14005811275What 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
14005811276σ(x-y)√(σ²x+σ²y) --> you add to get the difference because variance is distance from mean and you cannot have a negative distance52
14005811277calculate μx by handX1P1+X2P2+.... XKPK (SigmaXKPK)53
14005811278calculate var(x) by hand(X1-μx)²p(1)+(X2-μx)²p(2)+.... (Sigma(Xk-μx)²p(k))54
14005811279Standard deviationsquare root of variance55
14005811280discrete random variablesa fixed set of possible x values (whole numbers)56
14005811281continuous 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
14005811282What 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
14005811283mutually exclusiveno outcomes in common59
14005811284addition rule for mutually exclusive events P (A U B)P(A)+P(B)60
14005811285complement rule P(A^C)1-P(A)61
14005811286general addition rule (not mutually exclusive) P(A U B)P(A)+P(B)-P(A n B)62
14005811287intersection P(A n B)both A and B will occur63
14005811288conditional probability P (A | B)P(A n B) / P(B)64
14005811289independent events (how to check independence)P(A) = P(A|B) P(B)= P(B|A)65
14005811290multiplication rule for independent events P(A n B)P(A) x P(B)66
14005811291general multiplication rule (non-independent events) P(A n B)P(A) x P(B|A)67
14005811292sample spacea list of possible outcomes68
14005811293probability modela description of some chance process that consists of 2 parts: a sample space S and a probability for each outcome69
14005811294eventany collection of outcomes from some chance process, designated by a capital letter (an event is a subset of the sample space)70
14005811295What 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
14005811296Complementprobability that an event does not occur72
14005811297What is the sum of the probabilities of all possible outcomes?173
14005811298What is the probability of two mutually exclusive events?P(A U B)= P(A)+P(B)74
14005811299five 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
14005811300When is a two-way table helpfuldisplays the sample space for probabilities involving two events more clearly76
14005811301In statistics, what is meant by the word "or"?could have either event or both77
14005811302When can a Venn Diagram be helpful?visually represents the probabilities of not mutually exclusive events78
14005811303What 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
14005811304What does the intersection of two or more events mean?both event A and event B occur80
14005811305What does the union of two or more events mean?either event A or event B (or both) occurs81
14005811306What 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
14005811307the 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
14005811308How do you interpret a probability?We interpret probability to represent the most accurate results if we did an infinite amount of trials84
14005811309What 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
14005811310simulationthe imitation of chance behavior, based on a model that accurately reflects the situation86
14005811311Name 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
14005811312What 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
14005811313What does the intersection of two or more events mean?both event A and event B occur89
14005811314sampleThe part of the population from which we actually collect information. We use information from a sample to draw conclusions about the entire population90
14005811315populationIn a statistical study, this is the entire group of individuals about which we want information91
14005811316sample 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
14005811317convenience sampleA sample selected by taking the members of the population that are easiest to reach; particularly prone to large bias.93
14005811318biasThe design of a statistical study shows ______ if it systematically favors certain outcomes.94
14005811319voluntary response samplePeople decide whether to join a sample based on an open invitation; particularly prone to large bias.95
14005811320random samplingThe use of chance to select a sample; is the central principle of statistical sampling.96
14005811321simple random sample (SRS)every set of n individuals has an equal chance to be the sample actually selected97
14005811322strataGroups of individuals in a population that are similar in some way that might affect their responses.98
14005811323stratified 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
14005811324cluster 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
14005811325inferenceDrawing conclusions that go beyond the data at hand.101
14005811326margin of errorTells how close the estimate tends to be to the unknown parameter in repeated random sampling.102
14005811327sampling frameThe list from which a sample is actually chosen.103
14005811328undercoverageOccurs when some members of the population are left out of the sampling frame; a type of sampling error.104
14005811329nonresponseOccurs when a selected individual cannot be contacted or refuses to cooperate; an example of a nonsampling error.105
14005811330wording 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
14005811331observational studyObserves individuals and measures variables of interest but does not attempt to influence the responses.107
14005811332experimentDeliberately imposes some treatment on individuals to measure their responses.108
14005811333explanatory variableA variable that helps explain or influences changes in a response variable.109
14005811334response variableA variable that measures an outcome of a study.110
14005811335lurking variablea variable that is not among the explanatory or response variables in a study but that may influence the response variable.111
14005811336treatmentA 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
14005811337experimental unitthe smallest collection of individuals to which treatments are applied.113
14005811338subjectsExperimental units that are human beings.114
14005811339factorsthe explanatory variables in an experiment are often called this115
14005811340random 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
14005811341replicationAn 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
14005811342double-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
14005811343single-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
14005811344placeboan inactive (fake) treatment120
14005811345placebo effectDescribes the fact that some subjects respond favorably to any treatment, even an inactive one121
14005811346blockA 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
14005811347inference 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
14005811348inference 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
14005811349lack 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
14005811350institutional 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
14005811351informed 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
14005811352simulationa model of random events128
14005811353censusa sample that includes the entire population129
14005811354population parametera number that measures a characteristic of a population130
14005811355systematic sampleevery fifth individual, for example, is chosen131
14005811356multistage samplea sampling design where several sampling methods are combined132
14005811357sampling variabilitythe naturally occurring variability found in samples133
14005811358levelsthe values that the experimenter used for a factor134
14005811359the four principles of experimental designcontrol, randomization, replication, and blocking135
14005811360completely randomized designa design where all experimental units have an equal chance of receiving any treatment136
14005811361interpreting p valueif the true mean/proportion of the population is (null), the probability of getting a sample mean/proportion of _____ is (p-value).137
14005811362p̂1-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
14005811363probability of getting a certain p̂1-p̂2 (ex. less than .1)plug in center and spread into bell curve, find probability139
14005811364Confidence intervals for difference in proportions formula(p̂1-p̂2) plus or minus z*(√((p1(1-p1)/n1)+(p2(1-p2)/n2))140
14005811365When do you use t and z test/intervals?t for mean z for proportions141
14005811416Significance test for difference in proportions142
14005811366What is a null hypothesis?What is being claimed. Statistical test designed to assess strength of evidence against null hypothesis. Abbreviated by Ho.143
14005811367What is an alternative hypothesis?the claim about the population that we are trying to find evidence FOR, abbreviated by Ha144
14005811368When is the alternative hypothesis one-sided?Ha less than or greater than145
14005811369When is the alternative hypothesis two-sided?Ha is not equal to146
14005811370What is a significance level?fixed value that we compare with the P-value, matter of judgement to determine if something is "statistically significant".147
14005811371What is the default significance level?α=.05148
14005811372Interpreting 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
14005811373p value ≤ αWe reject our null hypothesis. There is sufficient evidence to say that (Ha) is true.150
14005811374p value ≥ αWe fail to reject our null hypothesis. There is insufficient evidence to say that (Ho) is not true.151
14005811375reject Ho when it is actually trueType I Error152
14005811376fail to reject Ho when it is actually falseType II Error153
14005811377Power definitionprobability of rejecting Ho when it is false154
14005811378probability of Type I Errorα155
14005811379probability of Type II Error1-power156
14005811380two ways to increase powerincrease sample size/significance level α157
140058113815 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
14005811417Formula for test statistic (μ)159
14005811382Formula for test statistic (p̂) (where p represents the null)(p̂-p)/(√((p)(1-p))/n)160
14005811383probability of a Type II Error?overlap normal distribution for null and true. Find rejection line. Use normalcdf161
14005811384when do you use z tests?for proportions162
14005811385when do you use t tests?for mean (population standard deviation unknown)163
14005811386finding p value for t teststcdf(min, max, df)164
14005811387Sample 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
14005811388What 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
14005811389When doing a paired t-test, to check normality, what do you do?check the differences histogram (μ1-μ2)167
14005811390How 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
14005811391How to interpret a C% Confidence IntervalWe are C% confident that the interval (_,_) will capture the true parameter (in context).169
14005811392What conditions must be checked before constructing a confidence interval?random, normal, independent170
14005811393C% 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
14005811418What's the z interval standard error formula?172
14005811394How do you find z*?InvNorm(#)173
14005811395How 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
14005811396How 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
14005811397Finding 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
14005811398Finding the confidence interval when the standard deviation of the population is *known*x bar +/- z*(σ/√n)177
14005811399Checking normal condition for z* (population standard deviation known)starts normal or CLT178
14005811400Finding the confidence interval when the standard deviation of the population is *unknown* (which is almost always true)x bar +/- t*(Sx/√n)179
14005811401degrees of freedomn-1180
14005811402How do you find t*?InvT(area to the left, df)181
14005811403What 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
14005811404a point estimator is a statistic that...provides an estimate of a population parameter.183
14005811405Explain the two conditions when the margin of error gets smaller.Confidence level C decreases, sample size n increases184
14005811406Does 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
14005811407Sx and σx: which is which?Sx is for a sample, σx is for a population186
14005811408How do we know when do use a t* interval instead of a z interval?you are not given the population standard deviation187
14005811409Checking 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
14005811410How 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
14005811411t* 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
14005811412margin of error formulaz* or t* (standard error)191
14005811413When 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
14005811414What is it looking for if it asks for the appropriate critical value?z/t* interval193

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