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9977215382How do you check if there is outliers?calculate IQR; anything above Q3+1.5(IQR) or below Q1-1.5(IQR) is an outlier0
9977215383If a graph is skewed, should we calculate the median or the mean? Why?median; it is resistant to skews and outliers1
9977215384If 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
9977215385What is in the five number summary?Minimum, Q1, Median, Q3, Maximum3
9977215386Relationship between variance and standard deviation?variance=(standard deviation)^24
9977215387variance definitionthe variance is roughly the average of the squared differences between each observation and the mean5
9977215388standard deviationthe standard deviation is the square root of the variance6
9977215389What should we use to measure spread if the median was calculated?IQR7
9977215390What should we use to measure spread if the mean was calculated?standard deviation8
9977215391What is the IQR? How much of the data does it represent?Q3-Q1; 50%9
9977215392How 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
9977215572What is the formula for standard deviation?11
9977215393Categorical variables vs. Quantitative VariablesCategorical: individuals can be assigned to one of several groups or categories Quantitative: takes numberical values12
9977215394If a possible outlier is on the fence, is it an outlier?No13
9977215395Things 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
9977215396Explain 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
9977215397What 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
9977215398What is a density curve?a curve that (a) is on or above the horizontal axis, and (b) has exactly an area of 117
9977215399Inverse Normwhen you want to find the percentile: invNorm (area, mean, standard deviation)18
9977215400z(x-mean)/standard deviation19
9977215401pth percentilethe value with p percent observations less than is20
9977215402cumulative relative frequency graphcan be used to describe the position of an individual within a distribution or to locate a specified percentile of the distribution21
9977215403How 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
9977215404rtells us the strength of a LINEAR association. -1 to 1. Not resistant to outliers23
9977215405r^2the proportion (percent) of the variation in the values of y that can be accounted for by the least squares regression line24
9977215406residual 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
9977215407regression 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
9977215408residual formularesidual=y-y(hat) aka observed y - predicted y27
9977215409What 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
9977215410What 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
9977215411nnumber of trials30
9977215412pprobability of success31
9977215413knumber of successes32
9977215414Binomial Formula for P(X=k)(n choose k) p^k (1-p)^(n-k)33
9977215415Binomial Calculator Function to find P(X=k)binompdf(n,p,k)34
9977215416Binomial Calculator Function for P(X≤k)binomcdf(n,p,k)35
9977215417Binomial Calculator Function for P(X≥k)1-binomcdf(n,p,k-1)36
9977215418mean of a binomial distributionnp37
9977215419standard deviation of a binomial distribution√(np(1-p))38
9977215420Geometric Formula for P(X=k)(1-p)^(k-1) x p39
9977215421Geometric Calculator Function to find P(X=k)geometpdf(p,k)40
9977215422Geometric Calculator Function for P(X≤k)geometcdf(p,k)41
9977215423Geometric Calculator Function for P(X≥k)1-geometcdf(p,k-1)42
9977215424Mean of a geometric distribution1/p=expected number of trials until success43
9977215425Standard deviation of a geometric distribution√((1-p)/(p²))44
9977215426What 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
9977215427how do you enter n choose k into the calculator?type "n" on home screen, go to MATH --> PRB --> 3: ncr, type "k"46
9977215428μ(x+y)μx+μy47
9977215429μ(x-y)μx-μy48
9977215430σ(x+y)√(σ²x+σ²y)49
9977215431What 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
9977215432What 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
9977215433σ(x-y)√(σ²x+σ²y) --> you add to get the difference because variance is distance from mean and you cannot have a negative distance52
9977215434calculate μx by handX1P1+X2P2+.... XKPK (SigmaXKPK)53
9977215435calculate var(x) by hand(X1-μx)²p(1)+(X2-μx)²p(2)+.... (Sigma(Xk-μx)²p(k))54
9977215436Standard deviationsquare root of variance55
9977215437discrete random variablesa fixed set of possible x values (whole numbers)56
9977215438continuous 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
9977215439What 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
9977215440mutually exclusiveno outcomes in common59
9977215441addition rule for mutually exclusive events P (A U B)P(A)+P(B)60
9977215442complement rule P(A^C)1-P(A)61
9977215443general addition rule (not mutually exclusive) P(A U B)P(A)+P(B)-P(A n B)62
9977215444intersection P(A n B)both A and B will occur63
9977215445conditional probability P (A | B)P(A n B) / P(B)64
9977215446independent events (how to check independence)P(A) = P(A|B) P(B)= P(B|A)65
9977215447multiplication rule for independent events P(A n B)P(A) x P(B)66
9977215448general multiplication rule (non-independent events) P(A n B)P(A) x P(B|A)67
9977215449sample spacea list of possible outcomes68
9977215450probability modela description of some chance process that consists of 2 parts: a sample space S and a probability for each outcome69
9977215451eventany collection of outcomes from some chance process, designated by a capital letter (an event is a subset of the sample space)70
9977215452What 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
9977215453Complementprobability that an event does not occur72
9977215454What is the sum of the probabilities of all possible outcomes?173
9977215455What is the probability of two mutually exclusive events?P(A U B)= P(A)+P(B)74
9977215456five 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
9977215457When is a two-way table helpfuldisplays the sample space for probabilities involving two events more clearly76
9977215458In statistics, what is meant by the word "or"?could have either event or both77
9977215459When can a Venn Diagram be helpful?visually represents the probabilities of not mutually exclusive events78
9977215460What 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
9977215461What does the intersection of two or more events mean?both event A and event B occur80
9977215462What does the union of two or more events mean?either event A or event B (or both) occurs81
9977215463What 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
9977215464the 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
9977215465How do you interpret a probability?We interpret probability to represent the most accurate results if we did an infinite amount of trials84
9977215466What 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
9977215467simulationthe imitation of chance behavior, based on a model that accurately reflects the situation86
9977215468Name 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
9977215469What 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
9977215470What does the intersection of two or more events mean?both event A and event B occur89
9977215471sampleThe part of the population from which we actually collect information. We use information from a sample to draw conclusions about the entire population90
9977215472populationIn a statistical study, this is the entire group of individuals about which we want information91
9977215473sample 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
9977215474convenience sampleA sample selected by taking the members of the population that are easiest to reach; particularly prone to large bias.93
9977215475biasThe design of a statistical study shows ______ if it systematically favors certain outcomes.94
9977215476voluntary response samplePeople decide whether to join a sample based on an open invitation; particularly prone to large bias.95
9977215477random samplingThe use of chance to select a sample; is the central principle of statistical sampling.96
9977215478simple random sample (SRS)every set of n individuals has an equal chance to be the sample actually selected97
9977215479strataGroups of individuals in a population that are similar in some way that might affect their responses.98
9977215480stratified 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
9977215481cluster 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
9977215482inferenceDrawing conclusions that go beyond the data at hand.101
9977215483margin of errorTells how close the estimate tends to be to the unknown parameter in repeated random sampling.102
9977215484sampling frameThe list from which a sample is actually chosen.103
9977215485undercoverageOccurs when some members of the population are left out of the sampling frame; a type of sampling error.104
9977215486nonresponseOccurs when a selected individual cannot be contacted or refuses to cooperate; an example of a nonsampling error.105
9977215487wording 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
9977215488observational studyObserves individuals and measures variables of interest but does not attempt to influence the responses.107
9977215489experimentDeliberately imposes some treatment on individuals to measure their responses.108
9977215490explanatory variableA variable that helps explain or influences changes in a response variable.109
9977215491response variableA variable that measures an outcome of a study.110
9977215492lurking variablea variable that is not among the explanatory or response variables in a study but that may influence the response variable.111
9977215493treatmentA 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
9977215494experimental unitthe smallest collection of individuals to which treatments are applied.113
9977215495subjectsExperimental units that are human beings.114
9977215496factorsthe explanatory variables in an experiment are often called this115
9977215497random 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
9977215498replicationAn 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
9977215499double-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
9977215500single-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
9977215501placeboan inactive (fake) treatment120
9977215502placebo effectDescribes the fact that some subjects respond favorably to any treatment, even an inactive one121
9977215503blockA 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
9977215504inference 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
9977215505inference 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
9977215506lack 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
9977215507institutional 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
9977215508informed 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
9977215509simulationa model of random events128
9977215510censusa sample that includes the entire population129
9977215511population parametera number that measures a characteristic of a population130
9977215512systematic sampleevery fifth individual, for example, is chosen131
9977215513multistage samplea sampling design where several sampling methods are combined132
9977215514sampling variabilitythe naturally occurring variability found in samples133
9977215515levelsthe values that the experimenter used for a factor134
9977215516the four principles of experimental designcontrol, randomization, replication, and blocking135
9977215517completely randomized designa design where all experimental units have an equal chance of receiving any treatment136
9977215518interpreting p valueif the true mean/proportion of the population is (null), the probability of getting a sample mean/proportion of _____ is (p-value).137
9977215519p̂1-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
9977215520probability of getting a certain p̂1-p̂2 (ex. less than .1)plug in center and spread into bell curve, find probability139
9977215521Confidence intervals for difference in proportions formula(p̂1-p̂2) plus or minus z*(√((p1(1-p1)/n1)+(p2(1-p2)/n2))140
9977215522When do you use t and z test/intervals?t for mean z for proportions141
9977215573Significance test for difference in proportions142
9977215523What is a null hypothesis?What is being claimed. Statistical test designed to assess strength of evidence against null hypothesis. Abbreviated by Ho.143
9977215524What is an alternative hypothesis?the claim about the population that we are trying to find evidence FOR, abbreviated by Ha144
9977215525When is the alternative hypothesis one-sided?Ha less than or greater than145
9977215526When is the alternative hypothesis two-sided?Ha is not equal to146
9977215527What is a significance level?fixed value that we compare with the P-value, matter of judgement to determine if something is "statistically significant".147
9977215528What is the default significance level?α=.05148
9977215529Interpreting 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
9977215530p value ≤ αWe reject our null hypothesis. There is sufficient evidence to say that (Ha) is true.150
9977215531p value ≥ αWe fail to reject our null hypothesis. There is insufficient evidence to say that (Ho) is not true.151
9977215532reject Ho when it is actually trueType I Error152
9977215533fail to reject Ho when it is actually falseType II Error153
9977215534Power definitionprobability of rejecting Ho when it is false154
9977215535probability of Type I Errorα155
9977215536probability of Type II Error1-power156
9977215537two ways to increase powerincrease sample size/significance level α157
99772155385 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
9977215574Formula for test statistic (μ)159
9977215539Formula for test statistic (p̂) (where p represents the null)(p̂-p)/(√((p)(1-p))/n)160
9977215540probability of a Type II Error?overlap normal distribution for null and true. Find rejection line. Use normalcdf161
9977215541when do you use z tests?for proportions162
9977215542when do you use t tests?for mean (population standard deviation unknown)163
9977215543finding p value for t teststcdf(min, max, df)164
9977215544Sample 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
9977215545What 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
9977215546When doing a paired t-test, to check normality, what do you do?check the differences histogram (μ1-μ2)167
9977215547How 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
9977215548How to interpret a C% Confidence IntervalWe are C% confident that the interval (_,_) will capture the true parameter (in context).169
9977215549What conditions must be checked before constructing a confidence interval?random, normal, independent170
9977215550C% 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
9977215575What's the z interval standard error formula?172
9977215551How do you find z*?InvNorm(#)173
9977215552How 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
9977215553How 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
9977215554Finding 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
9977215555Finding the confidence interval when the standard deviation of the population is *known*x bar +/- z*(σ/√n)177
9977215556Checking normal condition for z* (population standard deviation known)starts normal or CLT178
9977215557Finding the confidence interval when the standard deviation of the population is *unknown* (which is almost always true)x bar +/- t*(Sx/√n)179
9977215558degrees of freedomn-1180
9977215559How do you find t*?InvT(area to the left, df)181
9977215560What 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
9977215561a point estimator is a statistic that...provides an estimate of a population parameter.183
9977215562Explain the two conditions when the margin of error gets smaller.Confidence level C decreases, sample size n increases184
9977215563Does 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
9977215564Sx and σx: which is which?Sx is for a sample, σx is for a population186
9977215565How do we know when do use a t* interval instead of a z interval?you are not given the population standard deviation187
9977215566Checking 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
9977215567How 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
9977215568t* 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
9977215569margin of error formulaz* or t* (standard error)191
9977215570When 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
9977215571What is it looking for if it asks for the appropriate critical value?z/t* interval193

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