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13800172739How do you check if there is outliers?calculate IQR; anything above Q3+1.5(IQR) or below Q1-1.5(IQR) is an outlier0
13800172740If a graph is skewed, should we calculate the median or the mean? Why?median; it is resistant to skews and outliers1
13800172741If 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
13800172742What is in the five number summary?Minimum, Q1, Median, Q3, Maximum3
13800172743Relationship between variance and standard deviation?variance=(standard deviation)^24
13800172744variance definitionthe variance is roughly the average of the squared differences between each observation and the mean5
13800172745standard deviationthe standard deviation is the square root of the variance6
13800172746What should we use to measure spread if the median was calculated?IQR7
13800172747What should we use to measure spread if the mean was calculated?standard deviation8
13800172748What is the IQR? How much of the data does it represent?Q3-Q1; 50%9
13800172749How 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
13800172932What is the formula for standard deviation?11
13800172750Categorical variables vs. Quantitative VariablesCategorical: individuals can be assigned to one of several groups or categories Quantitative: takes numberical values12
13800172751If a possible outlier is on the fence, is it an outlier?No13
13800172752Things 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
13800172753Explain 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
13800172754What 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
13800172755What is a density curve?a curve that (a) is on or above the horizontal axis, and (b) has exactly an area of 117
13800172756Inverse Normwhen you want to find the percentile: invNorm (area, mean, standard deviation)18
13800172757z(x-mean)/standard deviation19
13800172758pth percentilethe value with p percent observations less than is20
13800172759cumulative relative frequency graphcan be used to describe the position of an individual within a distribution or to locate a specified percentile of the distribution21
13800172760How 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
13800172761rtells us the strength of a LINEAR association. -1 to 1. Not resistant to outliers23
13800172762r^2the proportion (percent) of the variation in the values of y that can be accounted for by the least squares regression line24
13800172763residual 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
13800172764regression 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
13800172765residual formularesidual=y-y(hat) aka observed y - predicted y27
13800172766What 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
13800172767What 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
13800172768nnumber of trials30
13800172769pprobability of success31
13800172770knumber of successes32
13800172771Binomial Formula for P(X=k)(n choose k) p^k (1-p)^(n-k)33
13800172772Binomial Calculator Function to find P(X=k)binompdf(n,p,k)34
13800172773Binomial Calculator Function for P(X≤k)binomcdf(n,p,k)35
13800172774Binomial Calculator Function for P(X≥k)1-binomcdf(n,p,k-1)36
13800172775mean of a binomial distributionnp37
13800172776standard deviation of a binomial distribution√(np(1-p))38
13800172777Geometric Formula for P(X=k)(1-p)^(k-1) x p39
13800172778Geometric Calculator Function to find P(X=k)geometpdf(p,k)40
13800172779Geometric Calculator Function for P(X≤k)geometcdf(p,k)41
13800172780Geometric Calculator Function for P(X≥k)1-geometcdf(p,k-1)42
13800172781Mean of a geometric distribution1/p=expected number of trials until success43
13800172782Standard deviation of a geometric distribution√((1-p)/(p²))44
13800172783What 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
13800172784how do you enter n choose k into the calculator?type "n" on home screen, go to MATH --> PRB --> 3: ncr, type "k"46
13800172785μ(x+y)μx+μy47
13800172786μ(x-y)μx-μy48
13800172787σ(x+y)√(σ²x+σ²y)49
13800172788What 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
13800172789What 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
13800172790σ(x-y)√(σ²x+σ²y) --> you add to get the difference because variance is distance from mean and you cannot have a negative distance52
13800172791calculate μx by handX1P1+X2P2+.... XKPK (SigmaXKPK)53
13800172792calculate var(x) by hand(X1-μx)²p(1)+(X2-μx)²p(2)+.... (Sigma(Xk-μx)²p(k))54
13800172793Standard deviationsquare root of variance55
13800172794discrete random variablesa fixed set of possible x values (whole numbers)56
13800172795continuous 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
13800172796What 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
13800172797mutually exclusiveno outcomes in common59
13800172798addition rule for mutually exclusive events P (A U B)P(A)+P(B)60
13800172799complement rule P(A^C)1-P(A)61
13800172800general addition rule (not mutually exclusive) P(A U B)P(A)+P(B)-P(A n B)62
13800172801intersection P(A n B)both A and B will occur63
13800172802conditional probability P (A | B)P(A n B) / P(B)64
13800172803independent events (how to check independence)P(A) = P(A|B) P(B)= P(B|A)65
13800172804multiplication rule for independent events P(A n B)P(A) x P(B)66
13800172805general multiplication rule (non-independent events) P(A n B)P(A) x P(B|A)67
13800172806sample spacea list of possible outcomes68
13800172807probability modela description of some chance process that consists of 2 parts: a sample space S and a probability for each outcome69
13800172808eventany collection of outcomes from some chance process, designated by a capital letter (an event is a subset of the sample space)70
13800172809What 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
13800172810Complementprobability that an event does not occur72
13800172811What is the sum of the probabilities of all possible outcomes?173
13800172812What is the probability of two mutually exclusive events?P(A U B)= P(A)+P(B)74
13800172813five 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
13800172814When is a two-way table helpfuldisplays the sample space for probabilities involving two events more clearly76
13800172815In statistics, what is meant by the word "or"?could have either event or both77
13800172816When can a Venn Diagram be helpful?visually represents the probabilities of not mutually exclusive events78
13800172817What 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
13800172818What does the intersection of two or more events mean?both event A and event B occur80
13800172819What does the union of two or more events mean?either event A or event B (or both) occurs81
13800172820What 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
13800172821the 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
13800172822How do you interpret a probability?We interpret probability to represent the most accurate results if we did an infinite amount of trials84
13800172823What 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
13800172824simulationthe imitation of chance behavior, based on a model that accurately reflects the situation86
13800172825Name 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
13800172826What 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
13800172827What does the intersection of two or more events mean?both event A and event B occur89
13800172828sampleThe part of the population from which we actually collect information. We use information from a sample to draw conclusions about the entire population90
13800172829populationIn a statistical study, this is the entire group of individuals about which we want information91
13800172830sample 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
13800172831convenience sampleA sample selected by taking the members of the population that are easiest to reach; particularly prone to large bias.93
13800172832biasThe design of a statistical study shows ______ if it systematically favors certain outcomes.94
13800172833voluntary response samplePeople decide whether to join a sample based on an open invitation; particularly prone to large bias.95
13800172834random samplingThe use of chance to select a sample; is the central principle of statistical sampling.96
13800172835simple random sample (SRS)every set of n individuals has an equal chance to be the sample actually selected97
13800172836strataGroups of individuals in a population that are similar in some way that might affect their responses.98
13800172837stratified 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
13800172838cluster 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
13800172839inferenceDrawing conclusions that go beyond the data at hand.101
13800172840margin of errorTells how close the estimate tends to be to the unknown parameter in repeated random sampling.102
13800172841sampling frameThe list from which a sample is actually chosen.103
13800172842undercoverageOccurs when some members of the population are left out of the sampling frame; a type of sampling error.104
13800172843nonresponseOccurs when a selected individual cannot be contacted or refuses to cooperate; an example of a nonsampling error.105
13800172844wording 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
13800172845observational studyObserves individuals and measures variables of interest but does not attempt to influence the responses.107
13800172846experimentDeliberately imposes some treatment on individuals to measure their responses.108
13800172847explanatory variableA variable that helps explain or influences changes in a response variable.109
13800172848response variableA variable that measures an outcome of a study.110
13800172849lurking variablea variable that is not among the explanatory or response variables in a study but that may influence the response variable.111
13800172850treatmentA 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
13800172851experimental unitthe smallest collection of individuals to which treatments are applied.113
13800172852subjectsExperimental units that are human beings.114
13800172853factorsthe explanatory variables in an experiment are often called this115
13800172854random 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
13800172855replicationAn 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
13800172856double-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
13800172857single-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
13800172858placeboan inactive (fake) treatment120
13800172859placebo effectDescribes the fact that some subjects respond favorably to any treatment, even an inactive one121
13800172860blockA 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
13800172861inference 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
13800172862inference 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
13800172863lack 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
13800172864institutional 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
13800172865informed 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
13800172866simulationa model of random events128
13800172867censusa sample that includes the entire population129
13800172868population parametera number that measures a characteristic of a population130
13800172869systematic sampleevery fifth individual, for example, is chosen131
13800172870multistage samplea sampling design where several sampling methods are combined132
13800172871sampling variabilitythe naturally occurring variability found in samples133
13800172872levelsthe values that the experimenter used for a factor134
13800172873the four principles of experimental designcontrol, randomization, replication, and blocking135
13800172874completely randomized designa design where all experimental units have an equal chance of receiving any treatment136
13800172875interpreting p valueif the true mean/proportion of the population is (null), the probability of getting a sample mean/proportion of _____ is (p-value).137
13800172876p̂1-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
13800172877probability of getting a certain p̂1-p̂2 (ex. less than .1)plug in center and spread into bell curve, find probability139
13800172878Confidence intervals for difference in proportions formula(p̂1-p̂2) plus or minus z*(√((p1(1-p1)/n1)+(p2(1-p2)/n2))140
13800172879When do you use t and z test/intervals?t for mean z for proportions141
13800172933Significance test for difference in proportions142
13800172880What is a null hypothesis?What is being claimed. Statistical test designed to assess strength of evidence against null hypothesis. Abbreviated by Ho.143
13800172881What is an alternative hypothesis?the claim about the population that we are trying to find evidence FOR, abbreviated by Ha144
13800172882When is the alternative hypothesis one-sided?Ha less than or greater than145
13800172883When is the alternative hypothesis two-sided?Ha is not equal to146
13800172884What is a significance level?fixed value that we compare with the P-value, matter of judgement to determine if something is "statistically significant".147
13800172885What is the default significance level?α=.05148
13800172886Interpreting 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
13800172887p value ≤ αWe reject our null hypothesis. There is sufficient evidence to say that (Ha) is true.150
13800172888p value ≥ αWe fail to reject our null hypothesis. There is insufficient evidence to say that (Ho) is not true.151
13800172889reject Ho when it is actually trueType I Error152
13800172890fail to reject Ho when it is actually falseType II Error153
13800172891Power definitionprobability of rejecting Ho when it is false154
13800172892probability of Type I Errorα155
13800172893probability of Type II Error1-power156
13800172894two ways to increase powerincrease sample size/significance level α157
138001728955 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
13800172934Formula for test statistic (μ)159
13800172896Formula for test statistic (p̂) (where p represents the null)(p̂-p)/(√((p)(1-p))/n)160
13800172897probability of a Type II Error?overlap normal distribution for null and true. Find rejection line. Use normalcdf161
13800172898when do you use z tests?for proportions162
13800172899when do you use t tests?for mean (population standard deviation unknown)163
13800172900finding p value for t teststcdf(min, max, df)164
13800172901Sample 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
13800172902What 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
13800172903When doing a paired t-test, to check normality, what do you do?check the differences histogram (μ1-μ2)167
13800172904How 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
13800172905How to interpret a C% Confidence IntervalWe are C% confident that the interval (_,_) will capture the true parameter (in context).169
13800172906What conditions must be checked before constructing a confidence interval?random, normal, independent170
13800172907C% 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
13800172935What's the z interval standard error formula?172
13800172908How do you find z*?InvNorm(#)173
13800172909How 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
13800172910How 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
13800172911Finding 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
13800172912Finding the confidence interval when the standard deviation of the population is *known*x bar +/- z*(σ/√n)177
13800172913Checking normal condition for z* (population standard deviation known)starts normal or CLT178
13800172914Finding the confidence interval when the standard deviation of the population is *unknown* (which is almost always true)x bar +/- t*(Sx/√n)179
13800172915degrees of freedomn-1180
13800172916How do you find t*?InvT(area to the left, df)181
13800172917What 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
13800172918a point estimator is a statistic that...provides an estimate of a population parameter.183
13800172919Explain the two conditions when the margin of error gets smaller.Confidence level C decreases, sample size n increases184
13800172920Does 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
13800172921Sx and σx: which is which?Sx is for a sample, σx is for a population186
13800172922How do we know when do use a t* interval instead of a z interval?you are not given the population standard deviation187
13800172923Checking 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
13800172924How 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
13800172925t* 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
13800172926margin of error formulaz* or t* (standard error)191
13800172927When 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
13800172928What is it looking for if it asks for the appropriate critical value?z/t* interval193

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