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13730106495How do you check if there is outliers?calculate IQR; anything above Q3+1.5(IQR) or below Q1-1.5(IQR) is an outlier0
13730106496If a graph is skewed, should we calculate the median or the mean? Why?median; it is resistant to skews and outliers1
13730106497If 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
13730106498What is in the five number summary?Minimum, Q1, Median, Q3, Maximum3
13730106499Relationship between variance and standard deviation?variance=(standard deviation)^24
13730106500variance definitionthe variance is roughly the average of the squared differences between each observation and the mean5
13730106501standard deviationthe standard deviation is the square root of the variance6
13730106502What should we use to measure spread if the median was calculated?IQR7
13730106503What should we use to measure spread if the mean was calculated?standard deviation8
13730106504What is the IQR? How much of the data does it represent?Q3-Q1; 50%9
13730106505How 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
13730106685What is the formula for standard deviation?11
13730106506Categorical variables vs. Quantitative VariablesCategorical: individuals can be assigned to one of several groups or categories Quantitative: takes numberical values12
13730106507If a possible outlier is on the fence, is it an outlier?No13
13730106508Things 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
13730106509Explain 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
13730106510What 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
13730106511What is a density curve?a curve that (a) is on or above the horizontal axis, and (b) has exactly an area of 117
13730106512Inverse Normwhen you want to find the percentile: invNorm (area, mean, standard deviation)18
13730106513z(x-mean)/standard deviation19
13730106514pth percentilethe value with p percent observations less than is20
13730106515cumulative relative frequency graphcan be used to describe the position of an individual within a distribution or to locate a specified percentile of the distribution21
13730106516How 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
13730106517rtells us the strength of a LINEAR association. -1 to 1. Not resistant to outliers23
13730106518r^2the proportion (percent) of the variation in the values of y that can be accounted for by the least squares regression line24
13730106519residual 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
13730106520regression 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
13730106521residual formularesidual=y-y(hat) aka observed y - predicted y27
13730106522What 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
13730106523What 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
13730106524nnumber of trials30
13730106525pprobability of success31
13730106526knumber of successes32
13730106527Binomial Formula for P(X=k)(n choose k) p^k (1-p)^(n-k)33
13730106528Binomial Calculator Function to find P(X=k)binompdf(n,p,k)34
13730106529Binomial Calculator Function for P(X≤k)binomcdf(n,p,k)35
13730106530Binomial Calculator Function for P(X≥k)1-binomcdf(n,p,k-1)36
13730106531mean of a binomial distributionnp37
13730106532standard deviation of a binomial distribution√(np(1-p))38
13730106533Geometric Formula for P(X=k)(1-p)^(k-1) x p39
13730106534Geometric Calculator Function to find P(X=k)geometpdf(p,k)40
13730106535Geometric Calculator Function for P(X≤k)geometcdf(p,k)41
13730106536Geometric Calculator Function for P(X≥k)1-geometcdf(p,k-1)42
13730106537Mean of a geometric distribution1/p=expected number of trials until success43
13730106538Standard deviation of a geometric distribution√((1-p)/(p²))44
13730106539What 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
13730106540how do you enter n choose k into the calculator?type "n" on home screen, go to MATH --> PRB --> 3: ncr, type "k"46
13730106541μ(x+y)μx+μy47
13730106542μ(x-y)μx-μy48
13730106543σ(x+y)√(σ²x+σ²y)49
13730106544What 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
13730106545What 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
13730106546σ(x-y)√(σ²x+σ²y) --> you add to get the difference because variance is distance from mean and you cannot have a negative distance52
13730106547calculate μx by handX1P1+X2P2+.... XKPK (SigmaXKPK)53
13730106548calculate var(x) by hand(X1-μx)²p(1)+(X2-μx)²p(2)+.... (Sigma(Xk-μx)²p(k))54
13730106549Standard deviationsquare root of variance55
13730106550discrete random variablesa fixed set of possible x values (whole numbers)56
13730106551continuous 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
13730106552What 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
13730106553mutually exclusiveno outcomes in common59
13730106554addition rule for mutually exclusive events P (A U B)P(A)+P(B)60
13730106555complement rule P(A^C)1-P(A)61
13730106556general addition rule (not mutually exclusive) P(A U B)P(A)+P(B)-P(A n B)62
13730106557intersection P(A n B)both A and B will occur63
13730106558conditional probability P (A | B)P(A n B) / P(B)64
13730106559independent events (how to check independence)P(A) = P(A|B) P(B)= P(B|A)65
13730106560multiplication rule for independent events P(A n B)P(A) x P(B)66
13730106561general multiplication rule (non-independent events) P(A n B)P(A) x P(B|A)67
13730106562sample spacea list of possible outcomes68
13730106563probability modela description of some chance process that consists of 2 parts: a sample space S and a probability for each outcome69
13730106564eventany collection of outcomes from some chance process, designated by a capital letter (an event is a subset of the sample space)70
13730106565What 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
13730106566Complementprobability that an event does not occur72
13730106567What is the sum of the probabilities of all possible outcomes?173
13730106568What is the probability of two mutually exclusive events?P(A U B)= P(A)+P(B)74
13730106569five 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
13730106570When is a two-way table helpfuldisplays the sample space for probabilities involving two events more clearly76
13730106571In statistics, what is meant by the word "or"?could have either event or both77
13730106572When can a Venn Diagram be helpful?visually represents the probabilities of not mutually exclusive events78
13730106573What 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
13730106574What does the intersection of two or more events mean?both event A and event B occur80
13730106575What does the union of two or more events mean?either event A or event B (or both) occurs81
13730106576What 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
13730106577the 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
13730106578How do you interpret a probability?We interpret probability to represent the most accurate results if we did an infinite amount of trials84
13730106579What 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
13730106580simulationthe imitation of chance behavior, based on a model that accurately reflects the situation86
13730106581Name 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
13730106582What 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
13730106583What does the intersection of two or more events mean?both event A and event B occur89
13730106584sampleThe part of the population from which we actually collect information. We use information from a sample to draw conclusions about the entire population90
13730106585populationIn a statistical study, this is the entire group of individuals about which we want information91
13730106586sample 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
13730106587convenience sampleA sample selected by taking the members of the population that are easiest to reach; particularly prone to large bias.93
13730106588biasThe design of a statistical study shows ______ if it systematically favors certain outcomes.94
13730106589voluntary response samplePeople decide whether to join a sample based on an open invitation; particularly prone to large bias.95
13730106590random samplingThe use of chance to select a sample; is the central principle of statistical sampling.96
13730106591simple random sample (SRS)every set of n individuals has an equal chance to be the sample actually selected97
13730106592strataGroups of individuals in a population that are similar in some way that might affect their responses.98
13730106593stratified 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
13730106594cluster 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
13730106595inferenceDrawing conclusions that go beyond the data at hand.101
13730106596margin of errorTells how close the estimate tends to be to the unknown parameter in repeated random sampling.102
13730106597sampling frameThe list from which a sample is actually chosen.103
13730106598undercoverageOccurs when some members of the population are left out of the sampling frame; a type of sampling error.104
13730106599nonresponseOccurs when a selected individual cannot be contacted or refuses to cooperate; an example of a nonsampling error.105
13730106600wording 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
13730106601observational studyObserves individuals and measures variables of interest but does not attempt to influence the responses.107
13730106602experimentDeliberately imposes some treatment on individuals to measure their responses.108
13730106603explanatory variableA variable that helps explain or influences changes in a response variable.109
13730106604response variableA variable that measures an outcome of a study.110
13730106605lurking variablea variable that is not among the explanatory or response variables in a study but that may influence the response variable.111
13730106606treatmentA 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
13730106607experimental unitthe smallest collection of individuals to which treatments are applied.113
13730106608subjectsExperimental units that are human beings.114
13730106609factorsthe explanatory variables in an experiment are often called this115
13730106610random 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
13730106611replicationAn 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
13730106612double-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
13730106613single-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
13730106614placeboan inactive (fake) treatment120
13730106615placebo effectDescribes the fact that some subjects respond favorably to any treatment, even an inactive one121
13730106616blockA 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
13730106617inference 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
13730106618inference 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
13730106619lack 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
13730106620institutional 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
13730106621informed 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
13730106622simulationa model of random events128
13730106623censusa sample that includes the entire population129
13730106624population parametera number that measures a characteristic of a population130
13730106625systematic sampleevery fifth individual, for example, is chosen131
13730106626sampling variabilitythe naturally occurring variability found in samples132
13730106627levelsthe values that the experimenter used for a factor133
13730106628the four principles of experimental designcontrol, randomization, replication, and blocking134
13730106629completely randomized designa design where all experimental units have an equal chance of receiving any treatment135
13730106630interpreting p valueif the true mean/proportion of the population is (null), the probability of getting a sample mean/proportion of _____ is (p-value).136
13730106631p̂1-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)137
13730106632probability of getting a certain p̂1-p̂2 (ex. less than .1)plug in center and spread into bell curve, find probability138
13730106633Confidence intervals for difference in proportions formula(p̂1-p̂2) plus or minus z*(√((p1(1-p1)/n1)+(p2(1-p2)/n2))139
13730106634When do you use t and z test/intervals?t for mean z for proportions140
13730106635What is a null hypothesis?What is being claimed. Statistical test designed to assess strength of evidence against null hypothesis. Abbreviated by Ho.141
13730106636What is an alternative hypothesis?the claim about the population that we are trying to find evidence FOR, abbreviated by Ha142
13730106637When is the alternative hypothesis one-sided?Ha less than or greater than143
13730106638When is the alternative hypothesis two-sided?Ha is not equal to144
13730106639What is a significance level?fixed value that we compare with the P-value, matter of judgement to determine if something is "statistically significant".145
13730106640What is the default significance level?α=.05146
13730106641Interpreting the p-valueif the true mean/proportion of the population is (null), the probability of getting a sample mean/proportion of _____ is (p-value).147
13730106642p value ≤ αWe reject our null hypothesis. There is sufficient evidence to say that (Ha) is true.148
13730106643p value ≥ αWe fail to reject our null hypothesis. There is insufficient evidence to say that (Ho) is not true.149
13730106644reject Ho when it is actually trueType I Error150
13730106645fail to reject Ho when it is actually falseType II Error151
13730106646Power definitionprobability of rejecting Ho when it is false152
13730106647probability of Type I Errorα153
13730106648probability of Type II Error1-power154
13730106649two ways to increase powerincrease sample size/significance level α155
137301066505 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 Ho156
13730106686Formula for test statistic (μ)157
13730106651Formula for test statistic (p̂) (where p represents the null)(p̂-p)/(√((p)(1-p))/n)158
13730106652probability of a Type II Error?overlap normal distribution for null and true. Find rejection line. Use normalcdf159
13730106653when do you use z tests?for proportions160
13730106654when do you use t tests?for mean (population standard deviation unknown)161
13730106655finding p value for t teststcdf(min, max, df)162
13730106656Sample 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 conclusion163
13730106657What 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 chance164
13730106658When doing a paired t-test, to check normality, what do you do?check the differences histogram (μ1-μ2)165
13730106659How 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).166
13730106660How to interpret a C% Confidence IntervalWe are C% confident that the interval (_,_) will capture the true parameter (in context).167
13730106661What conditions must be checked before constructing a confidence interval?random, normal, independent168
13730106662C% 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).169
13730106687What's the z interval standard error formula?170
13730106663How do you find z*?InvNorm(#)171
13730106664How 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)172
13730106665How 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 ends173
13730106666Finding 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=.5174
13730106667Finding the confidence interval when the standard deviation of the population is *known*x bar +/- z*(σ/√n)175
13730106668Checking normal condition for z* (population standard deviation known)starts normal or CLT176
13730106669Finding the confidence interval when the standard deviation of the population is *unknown* (which is almost always true)x bar +/- t*(Sx/√n)177
13730106670degrees of freedomn-1178
13730106671How do you find t*?InvT(area to the left, df)179
13730106672What 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)180
13730106673a point estimator is a statistic that...provides an estimate of a population parameter.181
13730106674Explain the two conditions when the margin of error gets smaller.Confidence level C decreases, sample size n increases182
13730106675Does 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 parameter183
13730106676Sx and σx: which is which?Sx is for a sample, σx is for a population184
13730106677How do we know when do use a t* interval instead of a z interval?you are not given the population standard deviation185
13730106678Checking 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)186
13730106679How 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)187
13730106680t* 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).188
13730106681margin of error formulaz* or t* (standard error)189
13730106682When 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 given190
13730106683What is it looking for if it asks for the appropriate critical value?z/t* interval191

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