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AP Statistics Review of Everything Flashcards

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9689519588How do you check if there is outliers?calculate IQR; anything above Q3+1.5(IQR) or below Q1-1.5(IQR) is an outlier0
9689519589If a graph is skewed, should we calculate the median or the mean? Why?median; it is resistant to skews and outliers1
9689519590If 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
9689519591What is in the five number summary?Minimum, Q1, Median, Q3, Maximum3
9689519592Relationship between variance and standard deviation?variance=(standard deviation)^24
9689519593variance definitionthe variance is roughly the average of the squared differences between each observation and the mean5
9689519594standard deviationthe standard deviation is the square root of the variance6
9689519595What should we use to measure spread if the median was calculated?IQR7
9689519596What should we use to measure spread if the mean was calculated?standard deviation8
9689519597What is the IQR? How much of the data does it represent?Q3-Q1; 50%9
9689519598How 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
9689519778What is the formula for standard deviation?11
9689519599Categorical variables vs. Quantitative VariablesCategorical: individuals can be assigned to one of several groups or categories Quantitative: takes numberical values12
9689519600If a possible outlier is on the fence, is it an outlier?No13
9689519601Things 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
9689519602Explain 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
9689519603What 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
9689519604What is a density curve?a curve that (a) is on or above the horizontal axis, and (b) has exactly an area of 117
9689519605Inverse Normwhen you want to find the percentile: invNorm (area, mean, standard deviation)18
9689519606z(x-mean)/standard deviation19
9689519607pth percentilethe value with p percent observations less than is20
9689519608cumulative relative frequency graphcan be used to describe the position of an individual within a distribution or to locate a specified percentile of the distribution21
9689519609How 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
9689519610rtells us the strength of a LINEAR association. -1 to 1. Not resistant to outliers23
9689519611r^2the proportion (percent) of the variation in the values of y that can be accounted for by the least squares regression line24
9689519612residual 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
9689519613regression 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
9689519614residual formularesidual=y-y(hat) aka observed y - predicted y27
9689519615What 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
9689519616What 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
9689519617nnumber of trials30
9689519618pprobability of success31
9689519619knumber of successes32
9689519620Binomial Formula for P(X=k)(n choose k) p^k (1-p)^(n-k)33
9689519621Binomial Calculator Function to find P(X=k)binompdf(n,p,k)34
9689519622Binomial Calculator Function for P(X≤k)binomcdf(n,p,k)35
9689519623Binomial Calculator Function for P(X≥k)1-binomcdf(n,p,k-1)36
9689519624mean of a binomial distributionnp37
9689519625standard deviation of a binomial distribution√(np(1-p))38
9689519626Geometric Formula for P(X=k)(1-p)^(k-1) x p39
9689519627Geometric Calculator Function to find P(X=k)geometpdf(p,k)40
9689519628Geometric Calculator Function for P(X≤k)geometcdf(p,k)41
9689519629Geometric Calculator Function for P(X≥k)1-geometcdf(p,k-1)42
9689519630Mean of a geometric distribution1/p=expected number of trials until success43
9689519631Standard deviation of a geometric distribution√((1-p)/(p²))44
9689519632What 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
9689519633how do you enter n choose k into the calculator?type "n" on home screen, go to MATH --> PRB --> 3: ncr, type "k"46
9689519634μ(x+y)μx+μy47
9689519635μ(x-y)μx-μy48
9689519636σ(x+y)√(σ²x+σ²y)49
9689519637What 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
9689519638What 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
9689519639σ(x-y)√(σ²x+σ²y) --> you add to get the difference because variance is distance from mean and you cannot have a negative distance52
9689519640calculate μx by handX1P1+X2P2+.... XKPK (SigmaXKPK)53
9689519641calculate var(x) by hand(X1-μx)²p(1)+(X2-μx)²p(2)+.... (Sigma(Xk-μx)²p(k))54
9689519642Standard deviationsquare root of variance55
9689519643discrete random variablesa fixed set of possible x values (whole numbers)56
9689519644continuous 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
9689519645What 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
9689519646mutually exclusiveno outcomes in common59
9689519647addition rule for mutually exclusive events P (A U B)P(A)+P(B)60
9689519648complement rule P(A^C)1-P(A)61
9689519649general addition rule (not mutually exclusive) P(A U B)P(A)+P(B)-P(A n B)62
9689519650intersection P(A n B)both A and B will occur63
9689519651conditional probability P (A | B)P(A n B) / P(B)64
9689519652independent events (how to check independence)P(A) = P(A|B) P(B)= P(B|A)65
9689519653multiplication rule for independent events P(A n B)P(A) x P(B)66
9689519654general multiplication rule (non-independent events) P(A n B)P(A) x P(B|A)67
9689519655sample spacea list of possible outcomes68
9689519656probability modela description of some chance process that consists of 2 parts: a sample space S and a probability for each outcome69
9689519657eventany collection of outcomes from some chance process, designated by a capital letter (an event is a subset of the sample space)70
9689519658What 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
9689519659Complementprobability that an event does not occur72
9689519660What is the sum of the probabilities of all possible outcomes?173
9689519661What is the probability of two mutually exclusive events?P(A U B)= P(A)+P(B)74
9689519662five 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
9689519663When is a two-way table helpfuldisplays the sample space for probabilities involving two events more clearly76
9689519664In statistics, what is meant by the word "or"?could have either event or both77
9689519665When can a Venn Diagram be helpful?visually represents the probabilities of not mutually exclusive events78
9689519666What 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
9689519667What does the intersection of two or more events mean?both event A and event B occur80
9689519668What does the union of two or more events mean?either event A or event B (or both) occurs81
9689519669What 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
9689519670the 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
9689519671How do you interpret a probability?We interpret probability to represent the most accurate results if we did an infinite amount of trials84
9689519672What 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
9689519673simulationthe imitation of chance behavior, based on a model that accurately reflects the situation86
9689519674Name 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
9689519675What 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
9689519676What does the intersection of two or more events mean?both event A and event B occur89
9689519677sampleThe part of the population from which we actually collect information. We use information from a sample to draw conclusions about the entire population90
9689519678populationIn a statistical study, this is the entire group of individuals about which we want information91
9689519679sample 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
9689519680convenience sampleA sample selected by taking the members of the population that are easiest to reach; particularly prone to large bias.93
9689519681biasThe design of a statistical study shows ______ if it systematically favors certain outcomes.94
9689519682voluntary response samplePeople decide whether to join a sample based on an open invitation; particularly prone to large bias.95
9689519683random samplingThe use of chance to select a sample; is the central principle of statistical sampling.96
9689519684simple random sample (SRS)every set of n individuals has an equal chance to be the sample actually selected97
9689519685strataGroups of individuals in a population that are similar in some way that might affect their responses.98
9689519686stratified 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
9689519687cluster 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
9689519688inferenceDrawing conclusions that go beyond the data at hand.101
9689519689margin of errorTells how close the estimate tends to be to the unknown parameter in repeated random sampling.102
9689519690sampling frameThe list from which a sample is actually chosen.103
9689519691undercoverageOccurs when some members of the population are left out of the sampling frame; a type of sampling error.104
9689519692nonresponseOccurs when a selected individual cannot be contacted or refuses to cooperate; an example of a nonsampling error.105
9689519693wording 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
9689519694observational studyObserves individuals and measures variables of interest but does not attempt to influence the responses.107
9689519695experimentDeliberately imposes some treatment on individuals to measure their responses.108
9689519696explanatory variableA variable that helps explain or influences changes in a response variable.109
9689519697response variableA variable that measures an outcome of a study.110
9689519698lurking variablea variable that is not among the explanatory or response variables in a study but that may influence the response variable.111
9689519699treatmentA 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
9689519700experimental unitthe smallest collection of individuals to which treatments are applied.113
9689519701subjectsExperimental units that are human beings.114
9689519702factorsthe explanatory variables in an experiment are often called this115
9689519703random 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
9689519704replicationAn 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
9689519705double-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
9689519706single-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
9689519707placeboan inactive (fake) treatment120
9689519708placebo effectDescribes the fact that some subjects respond favorably to any treatment, even an inactive one121
9689519709blockA 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
9689519710inference 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
9689519711inference 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
9689519712lack 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
9689519713institutional 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
9689519714informed 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
9689519715simulationa model of random events128
9689519716censusa sample that includes the entire population129
9689519717population parametera number that measures a characteristic of a population130
9689519718systematic sampleevery fifth individual, for example, is chosen131
9689519719multistage samplea sampling design where several sampling methods are combined132
9689519720sampling variabilitythe naturally occurring variability found in samples133
9689519721levelsthe values that the experimenter used for a factor134
9689519722the four principles of experimental designcontrol, randomization, replication, and blocking135
9689519723completely randomized designa design where all experimental units have an equal chance of receiving any treatment136
9689519724interpreting p valueif the true mean/proportion of the population is (null), the probability of getting a sample mean/proportion of _____ is (p-value).137
9689519725p̂1-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
9689519726probability of getting a certain p̂1-p̂2 (ex. less than .1)plug in center and spread into bell curve, find probability139
9689519727Confidence intervals for difference in proportions formula(p̂1-p̂2) plus or minus z*(√((p1(1-p1)/n1)+(p2(1-p2)/n2))140
9689519728When do you use t and z test/intervals?t for mean z for proportions141
9689519779Significance test for difference in proportions142
9689519729What is a null hypothesis?What is being claimed. Statistical test designed to assess strength of evidence against null hypothesis. Abbreviated by Ho.143
9689519730What is an alternative hypothesis?the claim about the population that we are trying to find evidence FOR, abbreviated by Ha144
9689519731When is the alternative hypothesis one-sided?Ha less than or greater than145
9689519732When is the alternative hypothesis two-sided?Ha is not equal to146
9689519733What is a significance level?fixed value that we compare with the P-value, matter of judgement to determine if something is "statistically significant".147
9689519734What is the default significance level?α=.05148
9689519735Interpreting 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
9689519736p value ≤ αWe reject our null hypothesis. There is sufficient evidence to say that (Ha) is true.150
9689519737p value ≥ αWe fail to reject our null hypothesis. There is insufficient evidence to say that (Ho) is not true.151
9689519738reject Ho when it is actually trueType I Error152
9689519739fail to reject Ho when it is actually falseType II Error153
9689519740Power definitionprobability of rejecting Ho when it is false154
9689519741probability of Type I Errorα155
9689519742probability of Type II Error1-power156
9689519743two ways to increase powerincrease sample size/significance level α157
96895197445 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
9689519780Formula for test statistic (μ)159
9689519745Formula for test statistic (p̂) (where p represents the null)(p̂-p)/(√((p)(1-p))/n)160
9689519746probability of a Type II Error?overlap normal distribution for null and true. Find rejection line. Use normalcdf161
9689519747when do you use z tests?for proportions162
9689519748when do you use t tests?for mean (population standard deviation unknown)163
9689519749finding p value for t teststcdf(min, max, df)164
9689519750Sample 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
9689519751What 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
9689519752When doing a paired t-test, to check normality, what do you do?check the differences histogram (μ1-μ2)167
9689519753How 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
9689519754How to interpret a C% Confidence IntervalWe are C% confident that the interval (_,_) will capture the true parameter (in context).169
9689519755What conditions must be checked before constructing a confidence interval?random, normal, independent170
9689519756C% confidence intervals of sample proportions, 4 step processState: Construct a C% confidence interval to estimate... Plan: one sample z-interval for proportions Check: Norma1 Do: Find the standard error and z*, then p hat +/- z* (1 sample z-proportions) Conclude: We are C% confident that the interval (_,_) will capture the true parameter (in context).171
9689519781What's the z interval standard error formula?172
9689519757How do you find z*?InvNorm(#)173
9689519758How 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
9689519759How 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
9689519760Finding 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
9689519761Finding the confidence interval when the standard deviation of the population is *known*x bar +/- z*(σ/√n)177
9689519762Checking normal condition for z* (population standard deviation known)starts normal or CLT178
9689519763Finding the confidence interval when the standard deviation of the population is *unknown* (which is almost always true)x bar +/- t*(Sx/√n)179
9689519764degrees of freedomn-1180
9689519765How do you find t*?t-table181
9689519766What 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
9689519767a point estimator is a statistic that...provides an estimate of a population parameter.183
9689519768Explain the two conditions when the margin of error gets smaller.Confidence level C decreases, sample size n increases184
9689519769Does 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
9689519770Sx and σx: which is which?Sx is for a sample, σx is for a population186
9689519771How do we know when do use a t* interval instead of a z interval?you are not given the population standard deviation187
9689519772Checking 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
9689519773How to check if a distribution is normal for t*, population n<15plug data into List 1, look at histogram. Conclude with "The boxplot looks roughly symmetric, so we should be safe to use the t distribution)189
9689519774t* confidence interval, 4 step processState: Construct a __% confidence interval to estimate... Plan: one sample t interval for a population mean Check: Normal (for Normal, look at sample size and go from there) Do: 1 sample t-interval Conclude: We are __% confident that the interval (_,_) will capture the true parameter (in context).190
9689519775margin of error formulaz* or t* (standard error)191
9689519776When 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*=t-table with df -population (n) will be given192
9689519777What is it looking for if it asks for the appropriate critical value?z/t* interval193

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