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9805820220How do you check if there is outliers?calculate IQR; anything above Q3+1.5(IQR) or below Q1-1.5(IQR) is an outlier0
9805820221If a graph is skewed, should we calculate the median or the mean? Why?median; it is resistant to skews and outliers1
9805820222If 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
9805820223What is in the five number summary?Minimum, Q1, Median, Q3, Maximum3
9805820224Relationship between variance and standard deviation?variance=(standard deviation)^24
9805820225variance definitionthe variance is roughly the average of the squared differences between each observation and the mean5
9805820226standard deviationthe standard deviation is the square root of the variance6
9805820227What should we use to measure spread if the median was calculated?IQR7
9805820228What should we use to measure spread if the mean was calculated?standard deviation8
9805820229What is the IQR? How much of the data does it represent?Q3-Q1; 50%9
9805820230How do you calculate standard deviation?1. Type data into L1 2. Find with 1 Variable Stats10
9805820231Categorical variables vs. Quantitative VariablesCategorical: individuals can be assigned to one of several groups or categories Quantitative: takes numberical values11
9805820233Things to include when describing a distributionShape (Roughly Symmetric, slightly/heavily skewed left or right, bimodal, range) Outliers Center (Mean or Median) Spread (Range, Standard Deviation or IQR)12
9805820234Explain how to standardize a variable. What is the purpose of standardizing a variable?Z- Score - Subtract the statistic from the parameter and then divide by standard deviation. Tells us how many standard deviations from the mean an observation falls, and in what direction.13
9805820235What 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 1 - Standard Normal Curve14
9805820236What is a density curve?a curve that (a) is on or above the horizontal axis, and (b) has exactly an area of 115
9805820237Inverse Normwhen you want to find the percentile: invNorm (area, mean, standard deviation)16
9805820238z(x-mean)/standard deviation17
9805820239pth percentilethe value with p percent observations less than is18
9805820240cumulative relative frequency graphcan be used to describe the position of an individual within a distribution or to locate a specified percentile of the distribution19
9805820241How to find and interpret the correlation coefficient r for a scatterplotMeasure of STRENGTH - value between -1 and 1 STAT plot, scatter, L1 and L2 (Plot 1: ON); STAT --> CALC --> 8:LinReg(a+bx) No r? --> 2nd 0 (Catalog) down to Diagnostic ON20
9805820242rtells us the strength of a LINEAR association. -1 to 1. Not resistant to outliers21
9805820243r^2the proportion (percent) of the variation in the values of y that can be accounted for by the least squares regression line22
9805820244residual 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 PATTERN23
9805820245regression 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.24
9805820246residual formularesidual=y-y(hat) aka actual y - predicted y25
9805820247What 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 trial26
9805820248What 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 trial27
9805820249nnumber of trials28
9805820250pprobability of success29
9805820251knumber of successes30
9805820252Binomial Formula for P(X=k)(n choose k) p^k (1-p)^(n-k)31
9805820253Binomial Calculator Function to find P(X=k)binompdf(n,p,k)32
9805820254Binomial Calculator Function for P(X≤k)binomcdf(n,p,k)33
9805820255Binomial Calculator Function for P(X≥k)1-binomcdf(n,p,k-1)34
9805820256mean of a binomial distributionnp35
9805820257standard deviation of a binomial distribution√(np(1-p))36
9805820258Geometric Formula for P(X=k)(1-p)^(k-1) x p37
9805820259Geometric Calculator Function to find P(X=k)geometpdf(p,k)38
9805820260Geometric Calculator Function for P(X≤k)geometcdf(p,k)39
9805820261Geometric Calculator Function for P(X≥k)1-geometcdf(p,k-1)40
9805820262Mean of a geometric distribution1/p=expected number of trials until success41
9805820263Standard deviation of a geometric distribution√((1-p)/(p²))42
9805820264What 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)43
9805820265how do you enter n choose k into the calculator?type "n" on home screen, go to MATH --> PRB --> 3: ncr, type "k"44
9805820266μ(x+y)μx+μy45
9805820267μ(x-y)μx-μy46
9805820268σ(x+y)√(σ²x+σ²y)47
9805820269What 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.48
9805820270What 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).49
9805820271σ(x-y)√(σ²x+σ²y) --> you add to get the difference because variance is distance from mean and you cannot have a negative distance50
9805820272calculate μx by handX1P1+X2P2+.... XKPK (SigmaXKPK)51
9805820273calculate var(x) by hand(X1-μx)²p(1)+(X2-μx)²p(2)+.... (Sigma(Xk-μx)²p(k))52
9805820274Standard deviationsquare root of variance53
9805820275discrete random variablesa fixed set of possible x values (whole numbers)54
9805820276continuous 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)55
9805820277What 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.56
9805820278mutually exclusiveno outcomes in common57
9805820279addition rule for mutually exclusive events P (A U B)P(A)+P(B)58
9805820280complement rule P(A^C)1-P(A)59
9805820281general addition rule (not mutually exclusive) P(A U B)P(A)+P(B)-P(A n B)60
9805820282intersection P(A n B)both A and B will occur61
9805820283conditional probability P (A | B)P(A n B) / P(B)62
9805820284independent events (how to check independence)P(A) = P(A|B) P(B)= P(B|A)63
9805820285multiplication rule for independent events P(A n B)P(A) x P(B)64
9805820286general multiplication rule (non-independent events) P(A n B)P(A) x P(B|A)65
9805820287sample spacea list of possible outcomes66
9805820288probability modela description of some chance process that consists of 2 parts: a sample space S and a probability for each outcome67
9805820289eventany collection of outcomes from some chance process, designated by a capital letter (an event is a subset of the sample space)68
9805820290What 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)69
9805820291Complementprobability that an event does not occur70
9805820292What is the sum of the probabilities of all possible outcomes?171
9805820293What is the probability of two mutually exclusive events?P(A U B)= P(A)+P(B)72
9805820294five 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)73
9805820295When is a two-way table helpfuldisplays the sample space for probabilities involving two events more clearly74
9805820296In statistics, what is meant by the word "or"?could have either event or both75
9805820297When can a Venn Diagram be helpful?visually represents the probabilities of not mutually exclusive events76
9805820298What 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)77
9805820299What does the intersection of two or more events mean?both event A and event B occur78
9805820300What does the union of two or more events mean?either event A or event B (or both) occurs79
9805820301What 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 outcome80
9805820302the 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 repetitions81
9805820303How do you interpret a probability?We interpret probability to represent the most accurate results if we did an infinite amount of trials82
9805820304What 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 outcome83
9805820305simulationthe imitation of chance behavior, based on a model that accurately reflects the situation84
9805820306Name 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 interest85
9805820307What 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 simulation86
9805820308What does the intersection of two or more events mean?both event A and event B occur87
9805820309sampleThe part of the population from which we actually collect information. We use information from a sample to draw conclusions about the entire population88
9805820310populationIn a statistical study, this is the entire group of individuals about which we want information89
9805820311sample 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.90
9805820312convenience sampleA sample selected by taking the members of the population that are easiest to reach; particularly prone to large bias.91
9805820313biasThe design of a statistical study shows ______ if it systematically favors certain outcomes.92
9805820314voluntary response samplePeople decide whether to join a sample based on an open invitation; particularly prone to large bias.93
9805820315random samplingThe use of chance to select a sample; is the central principle of statistical sampling.94
9805820316simple random sample (SRS)every set of n individuals has an equal chance to be the sample actually selected95
9805820317strataGroups of individuals in a population that are similar in some way that might affect their responses.96
9805820318stratified 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.97
9805820319cluster 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.98
9805820320inferenceDrawing conclusions that go beyond the data at hand.99
9805820321margin of errorTells how close the estimate tends to be to the unknown parameter in repeated random sampling.100
9805820322sampling frameThe list from which a sample is actually chosen.101
9805820323undercoverageOccurs when some members of the population are left out of the sampling frame; a type of sampling error.102
9805820324nonresponseOccurs when a selected individual cannot be contacted or refuses to cooperate; an example of a nonsampling error.103
9805820325wording 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.104
9805820326observational studyObserves individuals and measures variables of interest but does not attempt to influence the responses.105
9805820327experimentDeliberately imposes some treatment on individuals to measure their responses.106
9805820328explanatory variableA variable that helps explain or influences changes in a response variable.107
9805820329response variableA variable that measures an outcome of a study.108
9805820330lurking variablea variable that is not among the explanatory or response variables in a study but that may influence the response variable.109
9805820331treatmentA 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.110
9805820332experimental unitthe smallest collection of individuals to which treatments are applied.111
9805820333subjectsExperimental units that are human beings.112
9805820334factorsthe explanatory variables in an experiment are often called this113
9805820335random 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.114
9805820336replicationAn 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.115
9805820337double-blindAn experiment in which neither the subjects nor those who interact with them and measure the response variable know which treatment a subject received.116
9805820338single-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.117
9805820339placeboan inactive (fake) treatment118
9805820340placebo effectDescribes the fact that some subjects respond favorably to any treatment, even an inactive one119
9805820341blockA 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.120
9805820342inference 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.121
9805820343inference 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.122
9805820344lack 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.123
9805820345institutional 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.124
9805820346informed 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.125
9805820347simulationa model of random events126
9805820348censusa sample that includes the entire population127
9805820349population parametera number that measures a characteristic of a population128
9805820350systematic sampleevery fifth individual, for example, is chosen129
9805820351multistage samplea sampling design where several sampling methods are combined130
9805820352sampling variabilitythe naturally occurring variability found in samples131
9805820353levelsthe values that the experimenter used for a factor132
9805820354the four principles of experimental designcontrol, randomization, replication, and blocking133
9805820355completely randomized designa design where all experimental units have an equal chance of receiving any treatment134
9805820356interpreting p valueif the true mean/proportion of the population is (null), the probability of getting a sample mean/proportion of _____ is (p-value).135
9805820357p̂1-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)136
9805820358probability of getting a certain p̂1-p̂2 (ex. less than .1)plug in center and spread into bell curve, find probability137
9805820359Confidence intervals for difference in proportions formula(p̂1-p̂2) plus or minus z*(√((p1(1-p1)/n1)+(p2(1-p2)/n2))138
9805820360When do you use t and z test/intervals?t for mean z for proportions139
9805820411Significance test for difference in proportions140
9805820361What is a null hypothesis?What is being claimed. Statistical test designed to assess strength of evidence against null hypothesis. Abbreviated by Ho.141
9805820362What is an alternative hypothesis?the claim about the population that we are trying to find evidence FOR, abbreviated by Ha142
9805820363When is the alternative hypothesis one-sided?Ha less than or greater than143
9805820364When is the alternative hypothesis two-sided?Ha is not equal to144
9805820365What is a significance level?fixed value that we compare with the P-value, matter of judgement to determine if something is "statistically significant".145
9805820366What is the default significance level?α=.05146
9805820367Interpreting 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
9805820368p value ≤ αWe reject our null hypothesis. There is sufficient evidence to say that (Ha) is true.148
9805820369p value ≥ αWe fail to reject our null hypothesis. There is insufficient evidence to say that (Ho) is not true.149
9805820370reject Ho when it is actually trueType I Error150
9805820371fail to reject Ho when it is actually falseType II Error151
9805820372Power definitionprobability of rejecting Ho when it is false152
9805820373probability of Type I Errorα153
9805820374probability of Type II Error1-power154
9805820375two ways to increase powerincrease sample size/significance level α/increase effect size155
98058203765 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
9805820412Formula for test statistic (μ)t = x bar minus mu divided by (s over square root of n)157
9805820377Formula for test statistic (p̂) (where p represents the null)(p̂-p)/(√((p)(1-p))/n)158
9805820379when do you use z tests?for proportions159
9805820380when do you use t tests?for mean (population standard deviation unknown)160
9805820381finding p value for t tests when t is giventcdf(min, max, df)161
9805820382Sample 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 conclusion162
9805820383What 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 chance163
9805820384When doing a paired t-test, to check normality, what do you do?check the differences histogram (μ1-μ2)164
9805820385How 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).165
9805820386How to interpret a C% Confidence IntervalWe are C% confident that the interval (_,_) will capture the true parameter (in context).166
9805820387What conditions must be checked before constructing a confidence interval?random, normal, independent167
9805820388C% 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).168
9805820413What's the z interval standard error formula?169
9805820389How do you find z*?InvNorm(#)170
9805820390How 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)171
9805820391How 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 ends172
9805820392Finding 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=.5173
9805820393Finding the confidence interval when the standard deviation of the population is *known*x bar +/- z*(σ/√n)174
9805820394Checking normal condition for z* (population standard deviation known)starts normal or CLT175
9805820395Finding the confidence interval when the standard deviation of the population is *unknown* (which is almost always true)x bar +/- t*(Sx/√n)176
9805820396degrees of freedomn-1177
9805820397How do you find t*?InvT(area to the left, df)178
9805820398What 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)179
9805820399a point estimator is a statistic that...provides an estimate of a population parameter.180
9805820400Explain the two conditions when the margin of error gets smaller.Confidence level C decreases, sample size n increases181
9805820401Does 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 parameter182
9805820402Sx and σx: which is which?Sx is for a sample, σx is for a population183
9805820403How do we know when do use a t* interval instead of a z interval?you are not given the population standard deviation184
9805820404Checking 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)185
9805820405How 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)186
9805820406t* 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).187
9805820407margin of error formulaz* or t* (standard error)188
9805820408When 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 given189
9805820409What is it looking for if it asks for the appropriate critical value?z/t* interval190

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