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9877943445How do you check if there is outliers?calculate IQR; anything above Q3+1.5(IQR) or below Q1-1.5(IQR) is an outlier0
9877943446If a graph is skewed, should we calculate the median or the mean? Why?median; it is resistant to skews and outliers1
9877943447If 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
9877943448What is in the five number summary?Minimum, Q1, Median, Q3, Maximum3
9877943449Relationship between variance and standard deviation?variance=(standard deviation)^24
9877943450variance definitionthe variance is roughly the average of the squared differences between each observation and the mean5
9877943451standard deviationthe standard deviation is the square root of the variance6
9877943452What should we use to measure spread if the median was calculated?IQR7
9877943453What should we use to measure spread if the mean was calculated?standard deviation8
9877943454What is the IQR? How much of the data does it represent?Q3-Q1; 50%9
9877943455How 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
9877943635What is the formula for standard deviation?11
9877943456Categorical variables vs. Quantitative VariablesCategorical: individuals can be assigned to one of several groups or categories Quantitative: takes numberical values12
9877943457If a possible outlier is on the fence, is it an outlier?No13
9877943458Things 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
9877943459Explain 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
9877943460What 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
9877943461What is a density curve?a curve that (a) is on or above the horizontal axis, and (b) has exactly an area of 117
9877943462Inverse Normwhen you want to find the percentile: invNorm (area, mean, standard deviation)18
9877943463z(x-mean)/standard deviation19
9877943464pth percentilethe value with p percent observations less than is20
9877943465cumulative relative frequency graphcan be used to describe the position of an individual within a distribution or to locate a specified percentile of the distribution21
9877943466How 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
9877943467rtells us the strength of a LINEAR association. -1 to 1. Not resistant to outliers23
9877943468r^2the proportion (percent) of the variation in the values of y that can be accounted for by the least squares regression line24
9877943469residual 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
9877943470regression 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
9877943471residual formularesidual=y-y(hat) aka observed y - predicted y27
9877943472What 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
9877943473What 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
9877943474nnumber of trials30
9877943475pprobability of success31
9877943476knumber of successes32
9877943477Binomial Formula for P(X=k)(n choose k) p^k (1-p)^(n-k)33
9877943478Binomial Calculator Function to find P(X=k)binompdf(n,p,k)34
9877943479Binomial Calculator Function for P(X≤k)binomcdf(n,p,k)35
9877943480Binomial Calculator Function for P(X≥k)1-binomcdf(n,p,k-1)36
9877943481mean of a binomial distributionnp37
9877943482standard deviation of a binomial distribution√(np(1-p))38
9877943483Geometric Formula for P(X=k)(1-p)^(k-1) x p39
9877943484Geometric Calculator Function to find P(X=k)geometpdf(p,k)40
9877943485Geometric Calculator Function for P(X≤k)geometcdf(p,k)41
9877943486Geometric Calculator Function for P(X≥k)1-geometcdf(p,k-1)42
9877943487Mean of a geometric distribution1/p=expected number of trials until success43
9877943488Standard deviation of a geometric distribution√((1-p)/(p²))44
9877943489What 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
9877943490how do you enter n choose k into the calculator?type "n" on home screen, go to MATH --> PRB --> 3: ncr, type "k"46
9877943491μ(x+y)μx+μy47
9877943492μ(x-y)μx-μy48
9877943493σ(x+y)√(σ²x+σ²y)49
9877943494What 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
9877943495What 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
9877943496σ(x-y)√(σ²x+σ²y) --> you add to get the difference because variance is distance from mean and you cannot have a negative distance52
9877943497calculate μx by handX1P1+X2P2+.... XKPK (SigmaXKPK)53
9877943498calculate var(x) by hand(X1-μx)²p(1)+(X2-μx)²p(2)+.... (Sigma(Xk-μx)²p(k))54
9877943499Standard deviationsquare root of variance55
9877943500discrete random variablesa fixed set of possible x values (whole numbers)56
9877943501continuous 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
9877943502What 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
9877943503mutually exclusiveno outcomes in common59
9877943504addition rule for mutually exclusive events P (A U B)P(A)+P(B)60
9877943505complement rule P(A^C)1-P(A)61
9877943506general addition rule (not mutually exclusive) P(A U B)P(A)+P(B)-P(A n B)62
9877943507intersection P(A n B)both A and B will occur63
9877943508conditional probability P (A | B)P(A n B) / P(B)64
9877943509independent events (how to check independence)P(A) = P(A|B) P(B)= P(B|A)65
9877943510multiplication rule for independent events P(A n B)P(A) x P(B)66
9877943511general multiplication rule (non-independent events) P(A n B)P(A) x P(B|A)67
9877943512sample spacea list of possible outcomes68
9877943513probability modela description of some chance process that consists of 2 parts: a sample space S and a probability for each outcome69
9877943514eventany collection of outcomes from some chance process, designated by a capital letter (an event is a subset of the sample space)70
9877943515What 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
9877943516Complementprobability that an event does not occur72
9877943517What is the sum of the probabilities of all possible outcomes?173
9877943518What is the probability of two mutually exclusive events?P(A U B)= P(A)+P(B)74
9877943519five 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
9877943520When is a two-way table helpfuldisplays the sample space for probabilities involving two events more clearly76
9877943521In statistics, what is meant by the word "or"?could have either event or both77
9877943522When can a Venn Diagram be helpful?visually represents the probabilities of not mutually exclusive events78
9877943523What 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
9877943524What does the intersection of two or more events mean?both event A and event B occur80
9877943525What does the union of two or more events mean?either event A or event B (or both) occurs81
9877943526What 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
9877943527the 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
9877943528How do you interpret a probability?We interpret probability to represent the most accurate results if we did an infinite amount of trials84
9877943529What 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
9877943530simulationthe imitation of chance behavior, based on a model that accurately reflects the situation86
9877943531Name 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
9877943532What 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
9877943533What does the intersection of two or more events mean?both event A and event B occur89
9877943534sampleThe part of the population from which we actually collect information. We use information from a sample to draw conclusions about the entire population90
9877943535populationIn a statistical study, this is the entire group of individuals about which we want information91
9877943536sample 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
9877943537convenience sampleA sample selected by taking the members of the population that are easiest to reach; particularly prone to large bias.93
9877943538biasThe design of a statistical study shows ______ if it systematically favors certain outcomes.94
9877943539voluntary response samplePeople decide whether to join a sample based on an open invitation; particularly prone to large bias.95
9877943540random samplingThe use of chance to select a sample; is the central principle of statistical sampling.96
9877943541simple random sample (SRS)every set of n individuals has an equal chance to be the sample actually selected97
9877943542strataGroups of individuals in a population that are similar in some way that might affect their responses.98
9877943543stratified 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
9877943544cluster 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
9877943545inferenceDrawing conclusions that go beyond the data at hand.101
9877943546margin of errorTells how close the estimate tends to be to the unknown parameter in repeated random sampling.102
9877943547sampling frameThe list from which a sample is actually chosen.103
9877943548undercoverageOccurs when some members of the population are left out of the sampling frame; a type of sampling error.104
9877943549nonresponseOccurs when a selected individual cannot be contacted or refuses to cooperate; an example of a nonsampling error.105
9877943550wording 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
9877943551observational studyObserves individuals and measures variables of interest but does not attempt to influence the responses.107
9877943552experimentDeliberately imposes some treatment on individuals to measure their responses.108
9877943553explanatory variableA variable that helps explain or influences changes in a response variable.109
9877943554response variableA variable that measures an outcome of a study.110
9877943555lurking variablea variable that is not among the explanatory or response variables in a study but that may influence the response variable.111
9877943556treatmentA 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
9877943557experimental unitthe smallest collection of individuals to which treatments are applied.113
9877943558subjectsExperimental units that are human beings.114
9877943559factorsthe explanatory variables in an experiment are often called this115
9877943560random 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
9877943561replicationAn 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
9877943562double-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
9877943563single-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
9877943564placeboan inactive (fake) treatment120
9877943565placebo effectDescribes the fact that some subjects respond favorably to any treatment, even an inactive one121
9877943566blockA 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
9877943567inference 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
9877943568inference 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
9877943569lack 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
9877943570institutional 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
9877943571informed 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
9877943572simulationa model of random events128
9877943573censusa sample that includes the entire population129
9877943574population parametera number that measures a characteristic of a population130
9877943575systematic sampleevery fifth individual, for example, is chosen131
9877943576multistage samplea sampling design where several sampling methods are combined132
9877943577sampling variabilitythe naturally occurring variability found in samples133
9877943578levelsthe values that the experimenter used for a factor134
9877943579the four principles of experimental designcontrol, randomization, replication, and blocking135
9877943580completely randomized designa design where all experimental units have an equal chance of receiving any treatment136
9877943581interpreting p valueif the true mean/proportion of the population is (null), the probability of getting a sample mean/proportion of _____ is (p-value).137
9877943582p̂1-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
9877943583probability of getting a certain p̂1-p̂2 (ex. less than .1)plug in center and spread into bell curve, find probability139
9877943584Confidence intervals for difference in proportions formula(p̂1-p̂2) plus or minus z*(√((p1(1-p1)/n1)+(p2(1-p2)/n2))140
9877943585When do you use t and z test/intervals?t for mean z for proportions141
9877943636Significance test for difference in proportions142
9877943586What is a null hypothesis?What is being claimed. Statistical test designed to assess strength of evidence against null hypothesis. Abbreviated by Ho.143
9877943587What is an alternative hypothesis?the claim about the population that we are trying to find evidence FOR, abbreviated by Ha144
9877943588When is the alternative hypothesis one-sided?Ha less than or greater than145
9877943589When is the alternative hypothesis two-sided?Ha is not equal to146
9877943590What is a significance level?fixed value that we compare with the P-value, matter of judgement to determine if something is "statistically significant".147
9877943591What is the default significance level?α=.05148
9877943592Interpreting 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
9877943593p value ≤ αWe reject our null hypothesis. There is sufficient evidence to say that (Ha) is true.150
9877943594p value ≥ αWe fail to reject our null hypothesis. There is insufficient evidence to say that (Ho) is not true.151
9877943595reject Ho when it is actually trueType I Error152
9877943596fail to reject Ho when it is actually falseType II Error153
9877943597Power definitionprobability of rejecting Ho when it is false154
9877943598probability of Type I Errorα155
9877943599probability of Type II Error1-power156
9877943600two ways to increase powerincrease sample size/significance level α157
98779436015 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
9877943637Formula for test statistic (μ)159
9877943602Formula for test statistic (p̂) (where p represents the null)(p̂-p)/(√((p)(1-p))/n)160
9877943603probability of a Type II Error?overlap normal distribution for null and true. Find rejection line. Use normalcdf161
9877943604when do you use z tests?for proportions162
9877943605when do you use t tests?for mean (population standard deviation unknown)163
9877943606finding p value for t teststcdf(min, max, df)164
9877943607Sample 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
9877943608What 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
9877943609When doing a paired t-test, to check normality, what do you do?check the differences histogram (μ1-μ2)167
9877943610How 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
9877943611How to interpret a C% Confidence IntervalWe are C% confident that the interval (_,_) will capture the true parameter (in context).169
9877943612What conditions must be checked before constructing a confidence interval?random, normal, independent170
9877943613C% 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
9877943638What's the z interval standard error formula?172
9877943614How do you find z*?InvNorm(#)173
9877943615How 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
9877943616How 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
9877943617Finding 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
9877943618Finding the confidence interval when the standard deviation of the population is *known*x bar +/- z*(σ/√n)177
9877943619Checking normal condition for z* (population standard deviation known)starts normal or CLT178
9877943620Finding the confidence interval when the standard deviation of the population is *unknown* (which is almost always true)x bar +/- t*(Sx/√n)179
9877943621degrees of freedomn-1180
9877943622How do you find t*?InvT(area to the left, df)181
9877943623What 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
9877943624a point estimator is a statistic that...provides an estimate of a population parameter.183
9877943625Explain the two conditions when the margin of error gets smaller.Confidence level C decreases, sample size n increases184
9877943626Does 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
9877943627Sx and σx: which is which?Sx is for a sample, σx is for a population186
9877943628How do we know when do use a t* interval instead of a z interval?you are not given the population standard deviation187
9877943629Checking 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
9877943630How 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
9877943631t* 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
9877943632margin of error formulaz* or t* (standard error)191
9877943633When 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
9877943634What is it looking for if it asks for the appropriate critical value?z/t* interval193

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