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AP Statistics (Set 2) Flashcards

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9813734576How do you check if there is outliers?calculate IQR; anything above Q3+1.5(IQR) or below Q1-1.5(IQR) is an outlier0
9813734577If a graph is skewed, should we calculate the median or the mean? Why?median; it is resistant to skews and outliers1
9813734578If 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
9813734579What is in the five number summary?Minimum, Q1, Median, Q3, Maximum3
9813734580Relationship between variance and standard deviation?variance=(standard deviation)^24
9813734581variance definitionthe variance is roughly the average of the squared differences between each observation and the mean5
9813734582standard deviationthe standard deviation is the square root of the variance6
9813734583What should we use to measure spread if the median was calculated?IQR7
9813734584What should we use to measure spread if the mean was calculated?standard deviation8
9813734585What is the IQR? How much of the data does it represent?Q3-Q1; 50%9
9813734586How 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
9813734766What is the formula for standard deviation?11
9813734587Categorical variables vs. Quantitative VariablesCategorical: individuals can be assigned to one of several groups or categories Quantitative: takes numberical values12
9813734588If a possible outlier is on the fence, is it an outlier?No13
9813734589Things 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
9813734590Explain 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
9813734591What 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
9813734592What is a density curve?a curve that (a) is on or above the horizontal axis, and (b) has exactly an area of 117
9813734593Inverse Normwhen you want to find the percentile: invNorm (area, mean, standard deviation)18
9813734594z(x-mean)/standard deviation19
9813734595pth percentilethe value with p percent observations less than is20
9813734596cumulative relative frequency graphcan be used to describe the position of an individual within a distribution or to locate a specified percentile of the distribution21
9813734597How 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
9813734598rtells us the strength of a LINEAR association. -1 to 1. Not resistant to outliers23
9813734599r^2the proportion (percent) of the variation in the values of y that can be accounted for by the least squares regression line24
9813734600residual 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
9813734601regression 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
9813734602residual formularesidual=y-y(hat) aka observed y - predicted y27
9813734603What 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
9813734604What 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 (ex. you are waiting on your FIRST success) 4. Success: The probability of success equal in each trial29
9813734605nnumber of trials30
9813734606pprobability of success31
9813734607knumber of successes32
9813734608Binomial Formula for P(X=k)(n choose k) p^k (1-p)^(n-k)33
9813734609Binomial Calculator Function to find P(X=k)binompdf(n,p,k)34
9813734610Binomial Calculator Function for P(X≤k)binomcdf(n,p,k)35
9813734611Binomial Calculator Function for P(X≥k)1-binomcdf(n,p,k-1)36
9813734612mean of a binomial distributionnp37
9813734613standard deviation of a binomial distribution√(np(1-p))38
9813734614Geometric Formula for P(X=k)(1-p)^(k-1) x p39
9813734615Geometric Calculator Function to find P(X=k)geometpdf(p,k)40
9813734616Geometric Calculator Function for P(X≤k)geometcdf(p,k)41
9813734617Geometric Calculator Function for P(X≥k)1-geometcdf(p,k-1)42
9813734618Mean of a geometric distribution1/p=expected number of trials until success43
9813734619Standard deviation of a geometric distribution√((1-p)/(p²))44
9813734620What 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
9813734621how do you enter n choose k into the calculator?type "n" on home screen, go to MATH --> PRB --> 3: ncr, type "k"46
9813734622μ(x+y)μx+μy47
9813734623μ(x-y)μx-μy48
9813734624σ(x+y)√(σ²x+σ²y)49
9813734625What 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
9813734626What 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
9813734627σ(x-y)√(σ²x+σ²y) --> you add to get the difference because variance is distance from mean and you cannot have a negative distance52
9813734628calculate μx by handX1P1+X2P2+.... XKPK (SigmaXKPK)53
9813734629calculate var(x) by hand(X1-μx)²p(1)+(X2-μx)²p(2)+.... (Sigma(Xk-μx)²p(k))54
9813734630Standard deviationsquare root of variance55
9813734631discrete random variablesa fixed set of possible x values (whole numbers)56
9813734632continuous 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
9813734633What 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
9813734634mutually exclusiveno outcomes in common59
9813734635addition rule for mutually exclusive events P (A U B)P(A)+P(B)60
9813734636complement rule P(A^C)1-P(A)61
9813734637general addition rule (not mutually exclusive) P(A U B)P(A)+P(B)-P(A n B)62
9813734638intersection P(A n B)both A and B will occur63
9813734639conditional probability P (A | B)P(A n B) / P(B)64
9813734640independent events (how to check independence)P(A) = P(A|B) P(B)= P(B|A)65
9813734641multiplication rule for independent events P(A n B)P(A) x P(B)66
9813734642general multiplication rule (non-independent events) P(A n B)P(A) x P(B|A)67
9813734643sample spacea list of possible outcomes68
9813734644probability modela description of some chance process that consists of 2 parts: a sample space S and a probability for each outcome69
9813734645eventany collection of outcomes from some chance process, designated by a capital letter (an event is a subset of the sample space)70
9813734646What 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
9813734647Complementprobability that an event does not occur72
9813734648What is the sum of the probabilities of all possible outcomes?173
9813734649What is the probability of two mutually exclusive events?P(A U B)= P(A)+P(B)74
9813734650five 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
9813734651When is a two-way table helpfuldisplays the sample space for probabilities involving two events more clearly76
9813734652In statistics, what is meant by the word "or"?could have either event or both77
9813734653When can a Venn Diagram be helpful?visually represents the probabilities of not mutually exclusive events78
9813734654What 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
9813734655What does the intersection of two or more events mean?both event A and event B occur80
9813734656What does the union of two or more events mean?either event A or event B (or both) occurs81
9813734657What 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
9813734658the 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
9813734659How do you interpret a probability?We interpret probability to represent the most accurate results if we did an infinite amount of trials84
9813734660What 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
9813734661simulationthe imitation of chance behavior, based on a model that accurately reflects the situation86
9813734662Name 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
9813734663What 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
9813734664What does the intersection of two or more events mean?both event A and event B occur89
9813734665sampleThe part of the population from which we actually collect information. We use information from a sample to draw conclusions about the entire population90
9813734666populationIn a statistical study, this is the entire group of individuals about which we want information91
9813734667sample 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
9813734668convenience sampleA sample selected by taking the members of the population that are easiest to reach; particularly prone to large bias.93
9813734669biasThe design of a statistical study shows ______ if it systematically favors certain outcomes.94
9813734670voluntary response samplePeople decide whether to join a sample based on an open invitation; particularly prone to large bias.95
9813734671random samplingThe use of chance to select a sample; is the central principle of statistical sampling.96
9813734672simple random sample (SRS)every set of n individuals has an equal chance to be the sample actually selected97
9813734673strataGroups of individuals in a population that are similar in some way that might affect their responses.98
9813734674stratified 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
9813734675cluster 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
9813734676inferenceDrawing conclusions that go beyond the data at hand.101
9813734677margin of errorTells how close the estimate tends to be to the unknown parameter in repeated random sampling.102
9813734678sampling frameThe list from which a sample is actually chosen.103
9813734679undercoverageOccurs when some members of the population are left out of the sampling frame; a type of sampling error.104
9813734680nonresponseOccurs when a selected individual cannot be contacted or refuses to cooperate; an example of a nonsampling error.105
9813734681wording 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
9813734682observational studyObserves individuals and measures variables of interest but does not attempt to influence the responses.107
9813734683experimentDeliberately imposes some treatment on individuals to measure their responses.108
9813734684explanatory variableA variable that helps explain or influences changes in a response variable.109
9813734685response variableA variable that measures an outcome of a study.110
9813734686lurking variablea variable that is not among the explanatory or response variables in a study but that may influence the response variable.111
9813734687treatmentA 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
9813734688experimental unitthe smallest collection of individuals to which treatments are applied.113
9813734689subjectsExperimental units that are human beings.114
9813734690factorsthe explanatory variables in an experiment are often called this115
9813734691random 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
9813734692replicationAn 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
9813734693double-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
9813734694single-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
9813734695placeboan inactive (fake) treatment120
9813734696placebo effectDescribes the fact that some subjects respond favorably to any treatment, even an inactive one121
9813734697blockA 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
9813734698inference 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
9813734699inference 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
9813734700lack 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
9813734701institutional 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
9813734702informed 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
9813734703simulationa model of random events128
9813734704censusa sample that includes the entire population129
9813734705population parametera number that measures a characteristic of a population130
9813734706systematic sampleevery fifth individual, for example, is chosen131
9813734707multistage samplea sampling design where several sampling methods are combined132
9813734708sampling variabilitythe naturally occurring variability found in samples133
9813734709levelsthe values that the experimenter used for a factor134
9813734710the four principles of experimental designcontrol, randomization, replication, and blocking135
9813734711completely randomized designa design where all experimental units have an equal chance of receiving any treatment136
9813734712interpreting p valueif the true mean/proportion of the population is (null), the probability of getting a sample mean/proportion of _____ is (p-value).137
9813734713p̂1-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
9813734714probability of getting a certain p̂1-p̂2 (ex. less than .1)plug in center and spread into bell curve, find probability139
9813734715Confidence intervals for difference in proportions formula(p̂1-p̂2) plus or minus z*(√((p1(1-p1)/n1)+(p2(1-p2)/n2))140
9813734716When do you use t and z test/intervals?t for mean z for proportions141
9813734767Significance test for difference in proportions142
9813734717What is a null hypothesis?What is being claimed. Statistical test designed to assess strength of evidence against null hypothesis. Abbreviated by Ho.143
9813734718What is an alternative hypothesis?the claim about the population that we are trying to find evidence FOR, abbreviated by Ha144
9813734719When is the alternative hypothesis one-sided?Ha less than or greater than145
9813734720When is the alternative hypothesis two-sided?Ha is not equal to146
9813734721What is a significance level?fixed value that we compare with the P-value, matter of judgement to determine if something is "statistically significant".147
9813734722What is the default significance level?α=.05148
9813734723Interpreting 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
9813734724p value ≤ αWe reject our null hypothesis. There is sufficient evidence to say that (Ha) is true.150
9813734725p value ≥ αWe fail to reject our null hypothesis. There is insufficient evidence to say that (Ho) is not true.151
9813734726reject Ho when it is actually trueType I Error152
9813734727fail to reject Ho when it is actually falseType II Error153
9813734728Power definitionprobability of rejecting Ho when it is false154
9813734729probability of Type I Errorα155
9813734730probability of Type II Error1-power156
9813734731two ways to increase powerincrease sample size/significance level α157
98137347325 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
9813734768Formula for test statistic (μ)159
9813734733Formula for test statistic (p̂) (where p represents the null)(p̂-p)/(√((p)(1-p))/n)160
9813734734probability of a Type II Error?overlap normal distribution for null and true. Find rejection line. Use normalcdf161
9813734735when do you use z tests?for proportions162
9813734736when do you use t tests?for mean (population standard deviation unknown)163
9813734737finding p value for t teststcdf(min, max, df)164
9813734738Sample 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
9813734739What 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
9813734740When doing a paired t-test, to check normality, what do you do?check the differences histogram (μ1-μ2)167
9813734741How 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
9813734742How to interpret a C% Confidence IntervalWe are C% confident that the interval (_,_) will capture the true parameter (in context).169
9813734743What conditions must be checked before constructing a confidence interval?random, normal, independent170
9813734744C% 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
9813734769What's the z interval standard error formula?172
9813734745How do you find z*?InvNorm(#)173
9813734746How 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
9813734747How 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
9813734748Finding 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
9813734749Finding the confidence interval when the standard deviation of the population is *known*x bar +/- z*(σ/√n)177
9813734750Checking normal condition for z* (population standard deviation known)starts normal or CLT178
9813734751Finding the confidence interval when the standard deviation of the population is *unknown* (which is almost always true)x bar +/- t*(Sx/√n)179
9813734752degrees of freedomn-1180
9813734753How do you find t*?InvT(area to the left, df)181
9813734754What 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
9813734755a point estimator is a statistic that...provides an estimate of a population parameter.183
9813734756Explain the two conditions when the margin of error gets smaller.Confidence level C decreases, sample size n increases184
9813734757Does 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
9813734758Sx and σx: which is which?Sx is for a sample, σx is for a population186
9813734759How do we know when do use a t* interval instead of a z interval?you are not given the population standard deviation187
9813734760Checking 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
9813734761How 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
9813734762t* 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
9813734763margin of error formulaz* or t* (standard error)191
9813734764When 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
9813734765What is it looking for if it asks for the appropriate critical value?z/t* interval193

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