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13912195317How do you check if there is outliers?calculate IQR; anything above Q3+1.5(IQR) or below Q1-1.5(IQR) is an outlier0
13912195318If a graph is skewed, should we calculate the median or the mean? Why?median; it is resistant to skews and outliers1
13912195319If 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
13912195320What is in the five number summary?Minimum, Q1, Median, Q3, Maximum3
13912195321Relationship between variance and standard deviation?variance=(standard deviation)^24
13912195322variance definitionthe variance is roughly the average of the squared differences between each observation and the mean5
13912195323standard deviationthe standard deviation is the square root of the variance6
13912195324What should we use to measure spread if the median was calculated?IQR7
13912195325What should we use to measure spread if the mean was calculated?standard deviation8
13912195326What is the IQR? How much of the data does it represent?Q3-Q1; 50%9
13912195327How 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
13912195506What is the formula for standard deviation?11
13912195328Categorical variables vs. Quantitative VariablesCategorical: individuals can be assigned to one of several groups or categories Quantitative: takes numberical values12
13912195329If a possible outlier is on the fence, is it an outlier?No13
13912195330Things 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
13912195331Explain 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
13912195332What 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
13912195333What is a density curve?a curve that (a) is on or above the horizontal axis, and (b) has exactly an area of 117
13912195334Inverse Normwhen you want to find the percentile: invNorm (area, mean, standard deviation)18
13912195335z(x-mean)/standard deviation19
13912195336pth percentilethe value with p percent observations less than is20
13912195337cumulative relative frequency graphcan be used to describe the position of an individual within a distribution or to locate a specified percentile of the distribution21
13912195338How 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
13912195339rtells us the strength of a LINEAR association. -1 to 1. Not resistant to outliers23
13912195340r^2the proportion (percent) of the variation in the values of y that can be accounted for by the least squares regression line24
13912195341residual 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
13912195342regression 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
13912195343residual formularesidual=y-y(hat) aka observed y - predicted y27
13912195344What 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
13912195345What 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
13912195346nnumber of trials30
13912195347pprobability of success31
13912195348knumber of successes32
13912195349Binomial Formula for P(X=k)(n choose k) p^k (1-p)^(n-k)33
13912195350Binomial Calculator Function to find P(X=k)binompdf(n,p,k)34
13912195351Binomial Calculator Function for P(X≤k)binomcdf(n,p,k)35
13912195352Binomial Calculator Function for P(X≥k)1-binomcdf(n,p,k-1)36
13912195353mean of a binomial distributionnp37
13912195354standard deviation of a binomial distribution√(np(1-p))38
13912195355Geometric Formula for P(X=k)(1-p)^(k-1) x p39
13912195356Geometric Calculator Function to find P(X=k)geometpdf(p,k)40
13912195357Geometric Calculator Function for P(X≤k)geometcdf(p,k)41
13912195358Geometric Calculator Function for P(X≥k)1-geometcdf(p,k-1)42
13912195359Mean of a geometric distribution1/p=expected number of trials until success43
13912195360Standard deviation of a geometric distribution√((1-p)/(p²))44
13912195361What 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
13912195362how do you enter n choose k into the calculator?type "n" on home screen, go to MATH --> PRB --> 3: ncr, type "k"46
13912195363μ(x+y)μx+μy47
13912195364μ(x-y)μx-μy48
13912195365σ(x+y)√(σ²x+σ²y)49
13912195366What 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
13912195367What 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
13912195368σ(x-y)√(σ²x+σ²y) --> you add to get the difference because variance is distance from mean and you cannot have a negative distance52
13912195369calculate μx by handX1P1+X2P2+.... XKPK (SigmaXKPK)53
13912195370calculate var(x) by hand(X1-μx)²p(1)+(X2-μx)²p(2)+.... (Sigma(Xk-μx)²p(k))54
13912195371Standard deviationsquare root of variance55
13912195372discrete random variablesa fixed set of possible x values (whole numbers)56
13912195373continuous 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
13912195374What 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
13912195375mutually exclusiveno outcomes in common59
13912195376addition rule for mutually exclusive events P (A U B)P(A)+P(B)60
13912195377complement rule P(A^C)1-P(A)61
13912195378general addition rule (not mutually exclusive) P(A U B)P(A)+P(B)-P(A n B)62
13912195379intersection P(A n B)both A and B will occur63
13912195380conditional probability P (A | B)P(A n B) / P(B)64
13912195381independent events (how to check independence)P(A) = P(A|B) P(B)= P(B|A)65
13912195382multiplication rule for independent events P(A n B)P(A) x P(B)66
13912195383general multiplication rule (non-independent events) P(A n B)P(A) x P(B|A)67
13912195384sample spacea list of possible outcomes68
13912195385probability modela description of some chance process that consists of 2 parts: a sample space S and a probability for each outcome69
13912195386eventany collection of outcomes from some chance process, designated by a capital letter (an event is a subset of the sample space)70
13912195387What 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
13912195388Complementprobability that an event does not occur72
13912195389What is the sum of the probabilities of all possible outcomes?173
13912195390What is the probability of two mutually exclusive events?P(A U B)= P(A)+P(B)74
13912195391five 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
13912195392When is a two-way table helpfuldisplays the sample space for probabilities involving two events more clearly76
13912195393In statistics, what is meant by the word "or"?could have either event or both77
13912195394When can a Venn Diagram be helpful?visually represents the probabilities of not mutually exclusive events78
13912195395What 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
13912195396What does the intersection of two or more events mean?both event A and event B occur80
13912195397What does the union of two or more events mean?either event A or event B (or both) occurs81
13912195398What 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
13912195399the 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
13912195400How do you interpret a probability?We interpret probability to represent the most accurate results if we did an infinite amount of trials84
13912195401What 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
13912195402simulationthe imitation of chance behavior, based on a model that accurately reflects the situation86
13912195403Name 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
13912195404What 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
13912195405What does the intersection of two or more events mean?both event A and event B occur89
13912195406sampleThe part of the population from which we actually collect information. We use information from a sample to draw conclusions about the entire population90
13912195407populationIn a statistical study, this is the entire group of individuals about which we want information91
13912195408sample 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
13912195409convenience sampleA sample selected by taking the members of the population that are easiest to reach; particularly prone to large bias.93
13912195410biasThe design of a statistical study shows ______ if it systematically favors certain outcomes.94
13912195411voluntary response samplePeople decide whether to join a sample based on an open invitation; particularly prone to large bias.95
13912195412random samplingThe use of chance to select a sample; is the central principle of statistical sampling.96
13912195413simple random sample (SRS)every set of n individuals has an equal chance to be the sample actually selected97
13912195414strataGroups of individuals in a population that are similar in some way that might affect their responses.98
13912195415stratified 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
13912195416cluster 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
13912195417inferenceDrawing conclusions that go beyond the data at hand.101
13912195418margin of errorTells how close the estimate tends to be to the unknown parameter in repeated random sampling.102
13912195419sampling frameThe list from which a sample is actually chosen.103
13912195420undercoverageOccurs when some members of the population are left out of the sampling frame; a type of sampling error.104
13912195421nonresponseOccurs when a selected individual cannot be contacted or refuses to cooperate; an example of a nonsampling error.105
13912195422wording 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
13912195423observational studyObserves individuals and measures variables of interest but does not attempt to influence the responses.107
13912195424experimentDeliberately imposes some treatment on individuals to measure their responses.108
13912195425explanatory variableA variable that helps explain or influences changes in a response variable.109
13912195426response variableA variable that measures an outcome of a study.110
13912195427lurking variablea variable that is not among the explanatory or response variables in a study but that may influence the response variable.111
13912195428treatmentA 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
13912195429experimental unitthe smallest collection of individuals to which treatments are applied.113
13912195430subjectsExperimental units that are human beings.114
13912195431factorsthe explanatory variables in an experiment are often called this115
13912195432random 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
13912195433replicationAn 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
13912195434double-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
13912195435single-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
13912195436placeboan inactive (fake) treatment120
13912195437placebo effectDescribes the fact that some subjects respond favorably to any treatment, even an inactive one121
13912195438blockA 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
13912195439inference 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
13912195440inference 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
13912195441lack 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
13912195442institutional 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
13912195443informed 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
13912195444simulationa model of random events128
13912195445censusa sample that includes the entire population129
13912195446population parametera number that measures a characteristic of a population130
13912195447systematic sampleevery fifth individual, for example, is chosen131
13912195448sampling variabilitythe naturally occurring variability found in samples132
13912195449levelsthe values that the experimenter used for a factor133
13912195450the four principles of experimental designcontrol, randomization, replication, and blocking134
13912195451completely randomized designa design where all experimental units have an equal chance of receiving any treatment135
13912195452interpreting p valueif the true mean/proportion of the population is (null), the probability of getting a sample mean/proportion of _____ is (p-value).136
13912195453p̂1-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
13912195454probability of getting a certain p̂1-p̂2 (ex. less than .1)plug in center and spread into bell curve, find probability138
13912195455Confidence intervals for difference in proportions formula(p̂1-p̂2) plus or minus z*(√((p1(1-p1)/n1)+(p2(1-p2)/n2))139
13912195456When do you use t and z test/intervals?t for mean z for proportions140
13912195457What is a null hypothesis?What is being claimed. Statistical test designed to assess strength of evidence against null hypothesis. Abbreviated by Ho.141
13912195458What is an alternative hypothesis?the claim about the population that we are trying to find evidence FOR, abbreviated by Ha142
13912195459When is the alternative hypothesis one-sided?Ha less than or greater than143
13912195460When is the alternative hypothesis two-sided?Ha is not equal to144
13912195461What is a significance level?fixed value that we compare with the P-value, matter of judgement to determine if something is "statistically significant".145
13912195462What is the default significance level?α=.05146
13912195463Interpreting 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
13912195464p value ≤ αWe reject our null hypothesis. There is sufficient evidence to say that (Ha) is true.148
13912195465p value ≥ αWe fail to reject our null hypothesis. There is insufficient evidence to say that (Ho) is not true.149
13912195466reject Ho when it is actually trueType I Error150
13912195467fail to reject Ho when it is actually falseType II Error151
13912195468Power definitionprobability of rejecting Ho when it is false152
13912195469probability of Type I Errorα153
13912195470probability of Type II Error1-power154
13912195471two ways to increase powerincrease sample size/significance level α155
139121954725 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
13912195507Formula for test statistic (μ)157
13912195473Formula for test statistic (p̂) (where p represents the null)(p̂-p)/(√((p)(1-p))/n)158
13912195474probability of a Type II Error?overlap normal distribution for null and true. Find rejection line. Use normalcdf159
13912195475when do you use z tests?for proportions160
13912195476when do you use t tests?for mean (population standard deviation unknown)161
13912195477finding p value for t teststcdf(min, max, df)162
13912195478Sample 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
13912195479What 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
13912195480When doing a paired t-test, to check normality, what do you do?check the differences histogram (μ1-μ2)165
13912195481How 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
13912195482How to interpret a C% Confidence IntervalWe are C% confident that the interval (_,_) will capture the true parameter (in context).167
13912195483What conditions must be checked before constructing a confidence interval?random, normal, independent168
13912195484C% 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
13912195508What's the z interval standard error formula?170
13912195485How do you find z*?InvNorm(#)171
13912195486How 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
13912195487How 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
13912195488Finding 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
13912195489Finding the confidence interval when the standard deviation of the population is *known*x bar +/- z*(σ/√n)175
13912195490Checking normal condition for z* (population standard deviation known)starts normal or CLT176
13912195491Finding the confidence interval when the standard deviation of the population is *unknown* (which is almost always true)x bar +/- t*(Sx/√n)177
13912195492degrees of freedomn-1178
13912195493How do you find t*?InvT(area to the left, df)179
13912195494What 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
13912195495a point estimator is a statistic that...provides an estimate of a population parameter.181
13912195496Explain the two conditions when the margin of error gets smaller.Confidence level C decreases, sample size n increases182
13912195497Does 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
13912195498Sx and σx: which is which?Sx is for a sample, σx is for a population184
13912195499How do we know when do use a t* interval instead of a z interval?you are not given the population standard deviation185
13912195500Checking 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
13912195501How 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
13912195502t* 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
13912195503margin of error formulaz* or t* (standard error)189
13912195504When 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
13912195505What is it looking for if it asks for the appropriate critical value?z/t* interval191
13912203425Boxplotdisplays the 5-number summary as a central box with whiskers that extend to the non-outlying data values192
13912208152stem and leaf plotA method of graphing a collection of numbers by placing the "stem" digits (or initial digits) in one column and the "leaf" digits (or remaining digits) out to the right.193
13912217925HistogramA graph of vertical bars representing the frequency distribution of a set of data.194
13912221676Dot Plota graphical device that summarizes data by the number of dots above each data value on the horizontal axis195
13912225883Scatterplota graphed cluster of dots, each of which represents the values of two variables196

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