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6823514257calculate IQR; anything above Q3+1.5(IQR) or below Q1-1.5(IQR) is an outlierHow do you check if there is outliers?0
6823514258median; it is resistant to skews and outliersIf a graph is skewed, should we calculate the median or the mean? Why?1
6823514259mean; generally is more accurate if the data has no outliersIf a graph is roughly symmetrical, should we calculate the median or the mean? Why?2
6823514260Minimum, Q1, Median, Q3, MaximumWhat is in the five number summary?3
6823514261variance=(standard deviation)^2Relationship between variance and standard deviation?4
6823514262the variance is roughly the average of the squared differences between each observation and the meanvariance definition5
6823514263the standard deviation is the square root of the variancestandard deviation6
6823514264IQRWhat should we use to measure spread if the median was calculated?7
6823514265standard deviationWhat should we use to measure spread if the mean was calculated?8
6823514266Q3-Q1; 50%What is the IQR? How much of the data does it represent?9
68235142671. 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 itHow do you calculate standard deviation?10
6823514268What is the formula for standard deviation?11
6823514269Categorical: individuals can be assigned to one of several groups or categories Quantitative: takes numberical valuesCategorical variables vs. Quantitative Variables12
6823514270NoIf a possible outlier is on the fence, is it an outlier?13
6823514271Center (Mean or Median), Unusual Gaps or Outliers, Spread (Standard Deviation or IQR), Shape (Roughly Symmetric, slightly/heavily skewed left or right, bimodal, range)Things to include when describing a distribution14
6823514272Subtract 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.Explain how to standardize a variable. What is the purpose of standardizing a variable?15
6823514273shape would be the same as the original distribution, the mean would become 0, the standard deviation would become 1What effect does standardizing the values have on the distribution?16
6823514274a curve that (a) is on or above the horizontal axis, and (b) has exactly an area of 1What is a density curve?17
6823514275when you want to find the percentile: invNorm (area, mean, standard deviation)Inverse Norm18
6823514276(x-mean)/standard deviationz19
6823514277the value with p percent observations less than ispth percentile20
6823514278can be used to describe the position of an individual within a distribution or to locate a specified percentile of the distributioncumulative relative frequency graph21
6823514279STAT plot, scatter, L1 and L2 (Plot 1: ON); STAT --> CALC --> 8:LinReg(a+bx) No r? --> 2nd 0 (Catalog) down to Diagnostic ONHow to find and interpret the correlation coefficient r for a scatterplot22
6823514280tells us the strength of a LINEAR association. -1 to 1. Not resistant to outliersr23
6823514281the proportion (percent) of the variation in the values of y that can be accounted for by the least squares regression liner^224
6823514282a 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 PATTERNresidual plot25
6823514283a 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.regression line26
6823514284residual=y-y(hat) aka observed y - predicted yresidual formula27
6823514285BINS: 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 trialWhat method do you use to check if a distribution or probability is binomial?28
6823514286BITS: 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 trialWhat method do you use to check if a distribution or probability is geometric?29
6823514287number of trialsn30
6823514288probability of successp31
6823514289number of successesk32
6823514290(n choose k) p^k (1-p)^(n-k)Binomial Formula for P(X=k)33
6823514291binompdf(n,p,k)Binomial Calculator Function to find P(X=k)34
6823514292binomcdf(n,p,k)Binomial Calculator Function for P(X≤k)35
68235142931-binomcdf(n,p,k-1)Binomial Calculator Function for P(X≥k)36
6823514294npmean of a binomial distribution37
6823514295√(np(1-p))standard deviation of a binomial distribution38
6823514296(1-p)^(k-1) x pGeometric Formula for P(X=k)39
6823514297geometpdf(p,k)Geometric Calculator Function to find P(X=k)40
6823514298geometcdf(p,k)Geometric Calculator Function for P(X≤k)41
68235142991-geometcdf(p,k-1)Geometric Calculator Function for P(X≥k)42
68235143001/p=expected number of trials until successMean of a geometric distribution43
6823514301√((1-p)/(p²))Standard deviation of a geometric distribution44
6823514302Take binomcdf(n,p,maximum) - binomcdf(n,p,minimum-1)What do you do if the binomial probability is for a range, rather than a specific number?45
6823514303type "n" on home screen, go to MATH --> PRB --> 3: ncr, type "k"how do you enter n choose k into the calculator?46
6823514304Measures of center (median and mean). Does NOT affect measures of spread (IQR and Standard Deviation) or shape.What does adding or subtracting a constant effect?47
6823514305Both 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).What does multiplying or dividing a constant effect?48
6823514306√(σ²x+σ²y) --> you add to get the difference because variance is distance from mean and you cannot have a negative distanceσ(x-y)49
6823514307X1P1+X2P2+.... XKPK (SigmaXKPK)calculate μx by hand50
6823514308(X1-μx)²p(1)+(X2-μx)²p(2)+.... (Sigma(Xk-μx)²p(k))calculate var(x) by hand51
6823514309square root of varianceStandard deviation52
6823514310a fixed set of possible x values (whole numbers)discrete random variables53
6823514311-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)continuous random variables54
6823514312(σx)²+(σy)², but ONLY if x and y are independent.What is the variance of the sum of 2 random variables X and Y?55
6823514313no outcomes in commonmutually exclusive56
6823514314P(A)+P(B)addition rule for mutually exclusive events P (A U B)57
68235143151-P(A)complement rule P(A^C)58
6823514316P(A)+P(B)-P(A n B)general addition rule (not mutually exclusive) P(A U B)59
6823514317both A and B will occurintersection P(A n B)60
6823514318P(A n B) / P(B)conditional probability P (A | B)61
6823514319P(A) = P(A|B) P(B)= P(B|A)independent events (how to check independence)62
6823514320P(A) x P(B)multiplication rule for independent events P(A n B)63
6823514321P(A) x P(B|A)general multiplication rule (non-independent events) P(A n B)64
6823514322a list of possible outcomessample space65
6823514323a description of some chance process that consists of 2 parts: a sample space S and a probability for each outcomeprobability model66
6823514324any collection of outcomes from some chance process, designated by a capital letter (an event is a subset of the sample space)event67
6823514325P(A) = (number of outcomes corresponding to event A)/(total number of outcomes in sample space)What is the P(A) if all outcomes in the sample space are equally likely?68
6823514326probability that an event does not occurComplement69
68235143271What is the sum of the probabilities of all possible outcomes?70
6823514328P(A U B)= P(A)+P(B)What is the probability of two mutually exclusive events?71
68235143291. 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)five basic probability rules72
6823514330displays the sample space for probabilities involving two events more clearlyWhen is a two-way table helpful73
6823514331could have either event or bothIn statistics, what is meant by the word "or"?74
6823514332visually represents the probabilities of not mutually exclusive eventsWhen can a Venn Diagram be helpful?75
6823514333If 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)What is the general addition rule for two events?76
6823514334both event A and event B occurWhat does the intersection of two or more events mean?77
6823514335either event A or event B (or both) occursWhat does the union of two or more events mean?78
6823514336If 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 outcomeWhat is the law of large numbers?79
6823514337is a number between 0 and 1 that describes the proportion of times the outcome would occur in a very long series of repetitionsthe probability of any outcome...80
6823514338We interpret probability to represent the most accurate results if we did an infinite amount of trialsHow do you interpret a probability?81
68235143391. 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 outcomeWhat are the two myths about randomness?82
6823514340the imitation of chance behavior, based on a model that accurately reflects the situationsimulation83
68235143411. 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 interestName and describe the four steps in performing a simulation84
6823514342not providing a clear description of the simulation process for the reader to replicate the simulationWhat are some common errors when using a table of random digits?85
6823514343both event A and event B occurWhat does the intersection of two or more events mean?86
6823514344The part of the population from which we actually collect information. We use information from a sample to draw conclusions about the entire populationsample87
6823514345In a statistical study, this is the entire group of individuals about which we want informationpopulation88
6823514346A 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.sample survey89
6823514347A sample selected by taking the members of the population that are easiest to reach; particularly prone to large bias.convenience sample90
6823514348The design of a statistical study shows ______ if it systematically favors certain outcomes.bias91
6823514349People decide whether to join a sample based on an open invitation; particularly prone to large bias.voluntary response sample92
6823514350The use of chance to select a sample; is the central principle of statistical sampling.random sampling93
6823514351every set of n individuals has an equal chance to be the sample actually selectedsimple random sample (SRS)94
6823514352Groups of individuals in a population that are similar in some way that might affect their responses.strata95
6823514353To 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.stratified random sample96
6823514354To 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.cluster sample97
6823514355Drawing conclusions that go beyond the data at hand.inference98
6823514356Tells how close the estimate tends to be to the unknown parameter in repeated random sampling.margin of error99
6823514357The list from which a sample is actually chosen.sampling frame100
6823514358Occurs when some members of the population are left out of the sampling frame; a type of sampling error.undercoverage101
6823514359Occurs when a selected individual cannot be contacted or refuses to cooperate; an example of a nonsampling error.nonresponse102
6823514360The 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.wording of questions103
6823514361Observes individuals and measures variables of interest but does not attempt to influence the responses.observational study104
6823514362Deliberately imposes some treatment on individuals to measure their responses.experiment105
6823514363A variable that helps explain or influences changes in a response variable.explanatory variable106
6823514364A variable that measures an outcome of a study.response variable107
6823514365a variable that is not among the explanatory or response variables in a study but that may influence the response variable.lurking variable108
6823514366A 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.treatment109
6823514367the smallest collection of individuals to which treatments are applied.experimental unit110
6823514368Experimental units that are human beings.subjects111
6823514369the explanatory variables in an experiment are often called thisfactors112
6823514370An 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.random assignment113
6823514371An 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.replication114
6823514372An experiment in which neither the subjects nor those who interact with them and measure the response variable know which treatment a subject received.double-blind115
6823514373An 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.single-blind116
6823514374an inactive (fake) treatmentplacebo117
6823514375Describes the fact that some subjects respond favorably to any treatment, even an inactive oneplacebo effect118
6823514376A 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.block119
6823514377Using 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.inference about the population120
6823514378Using 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.inference about cause and effect121
6823514379When 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.lack of realism122
6823514380A 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.institutional review board123
6823514381A 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.informed consent124
6823514382a model of random eventssimulation125
6823514383a sample that includes the entire populationcensus126
6823514384a number that measures a characteristic of a populationpopulation parameter127
6823514385every fifth individual, for example, is chosensystematic sample128
6823514386a sampling design where several sampling methods are combinedmultistage sample129
6823514387the naturally occurring variability found in samplessampling variability130
6823514388the values that the experimenter used for a factorlevels131
6823514389control, randomization, replication, and blockingthe four principles of experimental design132
6823514390a design where all experimental units have an equal chance of receiving any treatmentcompletely randomized design133
6823514391if the true mean/proportion of the population is (null), the probability of getting a sample mean/proportion of _____ is (p-value).interpreting p value134
6823514392center: 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)p̂1-p̂2 center, shape, and spread135
6823514393plug in center and spread into bell curve, find probabilityprobability of getting a certain p̂1-p̂2 (ex. less than .1)136
6823514394(p̂1-p̂2) plus or minus z*(√((p1(1-p1)/n1)+(p2(1-p2)/n2))Confidence intervals for difference in proportions formula137
6823514395t for mean z for proportionsWhen do you use t and z test/intervals?138
6823514396Significance test for difference in proportions139
6823514397What is being claimed. Statistical test designed to assess strength of evidence against null hypothesis. Abbreviated by Ho.What is a null hypothesis?140
6823514398the claim about the population that we are trying to find evidence FOR, abbreviated by HaWhat is an alternative hypothesis?141
6823514399Ha less than or greater thanWhen is the alternative hypothesis one-sided?142
6823514400Ha is not equal toWhen is the alternative hypothesis two-sided?143
6823514401fixed value that we compare with the P-value, matter of judgement to determine if something is "statistically significant".What is a significance level?144
6823514402α=.05What is the default significance level?145
6823514403if the true mean/proportion of the population is (null), the probability of getting a sample mean/proportion of _____ is (p-value).Interpreting the p-value146
6823514404We reject our null hypothesis. There is sufficient evidence to say that (Ha) is true.p value ≤ α147
6823514405We fail to reject our null hypothesis. There is insufficient evidence to say that (Ho) is not true.p value ≥ α148
6823514406Type I Errorreject Ho when it is actually true149
6823514407Type II Errorfail to reject Ho when it is actually false150
6823514408probability of rejecting Ho when it is falsePower definition151
6823514409αprobability of Type I Error152
68235144101-powerprobability of Type II Error153
6823514411increase sample size/significance level αtwo ways to increase power154
6823514412State --> 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 Ho5 step process: z/t test155
6823514413Formula for test statistic (μ)156
6823514414(p̂-p)/(√((p)(1-p))/n)Formula for test statistic (p̂) (where p represents the null)157
6823514415overlap normal distribution for null and true. Find rejection line. Use normalcdfprobability of a Type II Error?158
6823514416for proportionswhen do you use z tests?159
6823514417for mean (population standard deviation unknown)when do you use t tests?160
6823514418tcdf(min, max, df)finding p value for t tests161
6823514419state--> 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 conclusionSample paired t test162
6823514420The sample mean/proportion is far enough away from the true mean/proportion that it couldn't have happened by chanceWhat does statistically significant mean in context of a problem?163
6823514421check the differences histogram (μ1-μ2)When doing a paired t-test, to check normality, what do you do?164
6823514422In C% of all possible samples of size n, we will construct an interval that captures the true parameter (in context).How to interpret a C% Confidence Level165
6823514423We are C% confident that the interval (_,_) will capture the true parameter (in context).How to interpret a C% Confidence Interval166
6823514424random, normal, independentWhat conditions must be checked before constructing a confidence interval?167
6823514425State: 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).C% confidence intervals of sample proportions, 5 step process168
6823514426What's the z interval standard error formula?169
6823514427InvNorm(#)How do you find z*?170
6823514428subtract the max and min confidence interval, divide it by two (aka find the mean of the interval ends)How do you find the point estimate of a sample?171
6823514429Ask, "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 endsHow do you find the margin of error, given the confidence interval?172
6823514430use p hat=.5Finding sample size proportions: When p hat is unknown, or you want to guarantee a margin of error less than or equal to:173
6823514431x bar +/- z*(σ/√n)Finding the confidence interval when the standard deviation of the population is *known*174
6823514432starts normal or CLTChecking normal condition for z* (population standard deviation known)175
6823514433x bar +/- t*(Sx/√n)Finding the confidence interval when the standard deviation of the population is *unknown* (which is almost always true)176
6823514434n-1degrees of freedom177
6823514435InvT(area to the left, df)How do you find t*?178
6823514436same as standard deviation, but we call it "standard error" because we plugged in p hat for p (we are estimating)What is the standard error?179
6823514437provides an estimate of a population parameter.a point estimator is a statistic that...180
6823514438Confidence level C decreases, sample size n increasesExplain the two conditions when the margin of error gets smaller.181
6823514439NO; the confidence interval gives us a set of plausible values for the parameterDoes the confidence level tell us the chance that a particular confidence interval captures the population parameter?182
6823514440Sx is for a sample, σx is for a populationSx and σx: which is which?183
6823514441you are not given the population standard deviationHow do we know when do use a t* interval instead of a z interval?184
6823514442Normal for sample size... -n -n<15: if the data appears closely normal (roughly symmetric, single peak, no outliers)Checking normal condition for t* (population standard deviation unknown)185
6823514443plug data into List 1, look at histogram. Conclude with "The histogram looks roughly symmetric, so we should be safe to use the t distribution)How to check if a distribution is normal for t*, population n<15186
6823514444State: 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).t* confidence interval, 5 step process187
6823514445z* or t* (standard error)margin of error formula188
6823514446x 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 givenWhen calculating t interval, what is it and where do you find the data?189
6823514447z/t* intervalWhat is it looking for if it asks for the appropriate critical value?190

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