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10434845346How do you check if there is outliers?calculate IQR; anything above Q3+1.5(IQR) or below Q1-1.5(IQR) is an outlier0
10434845347If a graph is skewed, should we calculate the median or the mean? Why?median; it is resistant to skews and outliers1
10434845348If 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
10434845349What is in the five number summary?Minimum, Q1, Median, Q3, Maximum3
10434845350Relationship between variance and standard deviation?variance=(standard deviation)^24
10434845351variance definitionthe variance is roughly the average of the squared differences between each observation and the mean5
10434845352standard deviationthe standard deviation is the square root of the variance6
10434845353What should we use to measure spread if the median was calculated?IQR7
10434845354What should we use to measure spread if the mean was calculated?standard deviation8
10434845355What is the IQR? How much of the data does it represent?Q3-Q1; 50%9
10434845356How 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
10434845536What is the formula for standard deviation?11
10434845357Categorical variables vs. Quantitative VariablesCategorical: individuals can be assigned to one of several groups or categories Quantitative: takes numberical values12
10434845358If a possible outlier is on the fence, is it an outlier?No13
10434845359Things 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
10434845360Explain 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
10434845361What 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
10434845362What is a density curve?a curve that (a) is on or above the horizontal axis, and (b) has exactly an area of 117
10434845363Inverse Normwhen you want to find the percentile: invNorm (area, mean, standard deviation)18
10434845364z(x-mean)/standard deviation19
10434845365pth percentilethe value with p percent observations less than is20
10434845366cumulative relative frequency graphcan be used to describe the position of an individual within a distribution or to locate a specified percentile of the distribution21
10434845367How 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
10434845368rtells us the strength of a LINEAR association. -1 to 1. Not resistant to outliers23
10434845369r^2the proportion (percent) of the variation in the values of y that can be accounted for by the least squares regression line24
10434845370residual 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
10434845371regression 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
10434845372residual formularesidual=y-y(hat) aka observed y - predicted y27
10434845373What 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
10434845374What 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
10434845375nnumber of trials30
10434845376pprobability of success31
10434845377knumber of successes32
10434845378Binomial Formula for P(X=k)(n choose k) p^k (1-p)^(n-k)33
10434845379Binomial Calculator Function to find P(X=k)binompdf(n,p,k)34
10434845380Binomial Calculator Function for P(X≤k)binomcdf(n,p,k)35
10434845381Binomial Calculator Function for P(X≥k)1-binomcdf(n,p,k-1)36
10434845382mean of a binomial distributionnp37
10434845383standard deviation of a binomial distribution√(np(1-p))38
10434845384Geometric Formula for P(X=k)(1-p)^(k-1) x p39
10434845385Geometric Calculator Function to find P(X=k)geometpdf(p,k)40
10434845386Geometric Calculator Function for P(X≤k)geometcdf(p,k)41
10434845387Geometric Calculator Function for P(X≥k)1-geometcdf(p,k-1)42
10434845388Mean of a geometric distribution1/p=expected number of trials until success43
10434845389Standard deviation of a geometric distribution√((1-p)/(p²))44
10434845390What 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
10434845391how do you enter n choose k into the calculator?type "n" on home screen, go to MATH --> PRB --> 3: ncr, type "k"46
10434845392μ(x+y)μx+μy47
10434845393μ(x-y)μx-μy48
10434845394σ(x+y)√(σ²x+σ²y)49
10434845395What 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
10434845396What 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
10434845397σ(x-y)√(σ²x+σ²y) --> you add to get the difference because variance is distance from mean and you cannot have a negative distance52
10434845398calculate μx by handX1P1+X2P2+.... XKPK (SigmaXKPK)53
10434845399calculate var(x) by hand(X1-μx)²p(1)+(X2-μx)²p(2)+.... (Sigma(Xk-μx)²p(k))54
10434845400Standard deviationsquare root of variance55
10434845401discrete random variablesa fixed set of possible x values (whole numbers)56
10434845402continuous 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
10434845403What 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
10434845404mutually exclusiveno outcomes in common59
10434845405addition rule for mutually exclusive events P (A U B)P(A)+P(B)60
10434845406complement rule P(A^C)1-P(A)61
10434845407general addition rule (not mutually exclusive) P(A U B)P(A)+P(B)-P(A n B)62
10434845408intersection P(A n B)both A and B will occur63
10434845409conditional probability P (A | B)P(A n B) / P(B)64
10434845410independent events (how to check independence)P(A) = P(A|B) P(B)= P(B|A)65
10434845411multiplication rule for independent events P(A n B)P(A) x P(B)66
10434845412general multiplication rule (non-independent events) P(A n B)P(A) x P(B|A)67
10434845413sample spacea list of possible outcomes68
10434845414probability modela description of some chance process that consists of 2 parts: a sample space S and a probability for each outcome69
10434845415eventany collection of outcomes from some chance process, designated by a capital letter (an event is a subset of the sample space)70
10434845416What 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
10434845417Complementprobability that an event does not occur72
10434845418What is the sum of the probabilities of all possible outcomes?173
10434845419What is the probability of two mutually exclusive events?P(A U B)= P(A)+P(B)74
10434845420five 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
10434845421When is a two-way table helpfuldisplays the sample space for probabilities involving two events more clearly76
10434845422In statistics, what is meant by the word "or"?could have either event or both77
10434845423When can a Venn Diagram be helpful?visually represents the probabilities of not mutually exclusive events78
10434845424What 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
10434845425What does the intersection of two or more events mean?both event A and event B occur80
10434845426What does the union of two or more events mean?either event A or event B (or both) occurs81
10434845427What 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
10434845428the 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
10434845429How do you interpret a probability?We interpret probability to represent the most accurate results if we did an infinite amount of trials84
10434845430What 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
10434845431simulationthe imitation of chance behavior, based on a model that accurately reflects the situation86
10434845432Name 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
10434845433What 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
10434845434What does the intersection of two or more events mean?both event A and event B occur89
10434845435sampleThe part of the population from which we actually collect information. We use information from a sample to draw conclusions about the entire population90
10434845436populationIn a statistical study, this is the entire group of individuals about which we want information91
10434845437sample 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
10434845438convenience sampleA sample selected by taking the members of the population that are easiest to reach; particularly prone to large bias.93
10434845439biasThe design of a statistical study shows ______ if it systematically favors certain outcomes.94
10434845440voluntary response samplePeople decide whether to join a sample based on an open invitation; particularly prone to large bias.95
10434845441random samplingThe use of chance to select a sample; is the central principle of statistical sampling.96
10434845442simple random sample (SRS)every set of n individuals has an equal chance to be the sample actually selected97
10434845443strataGroups of individuals in a population that are similar in some way that might affect their responses.98
10434845444stratified 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
10434845445cluster 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
10434845446inferenceDrawing conclusions that go beyond the data at hand.101
10434845447margin of errorTells how close the estimate tends to be to the unknown parameter in repeated random sampling.102
10434845448sampling frameThe list from which a sample is actually chosen.103
10434845449undercoverageOccurs when some members of the population are left out of the sampling frame; a type of sampling error.104
10434845450nonresponseOccurs when a selected individual cannot be contacted or refuses to cooperate; an example of a nonsampling error.105
10434845451wording 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
10434845452observational studyObserves individuals and measures variables of interest but does not attempt to influence the responses.107
10434845453experimentDeliberately imposes some treatment on individuals to measure their responses.108
10434845454explanatory variableA variable that helps explain or influences changes in a response variable.109
10434845455response variableA variable that measures an outcome of a study.110
10434845456lurking variablea variable that is not among the explanatory or response variables in a study but that may influence the response variable.111
10434845457treatmentA 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
10434845458experimental unitthe smallest collection of individuals to which treatments are applied.113
10434845459subjectsExperimental units that are human beings.114
10434845460factorsthe explanatory variables in an experiment are often called this115
10434845461random 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
10434845462replicationAn 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
10434845463double-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
10434845464single-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
10434845465placeboan inactive (fake) treatment120
10434845466placebo effectDescribes the fact that some subjects respond favorably to any treatment, even an inactive one121
10434845467blockA 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
10434845468inference 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
10434845469inference 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
10434845470lack 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
10434845471institutional 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
10434845472informed 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
10434845473simulationa model of random events128
10434845474censusa sample that includes the entire population129
10434845475population parametera number that measures a characteristic of a population130
10434845476systematic sampleevery fifth individual, for example, is chosen131
10434845477multistage samplea sampling design where several sampling methods are combined132
10434845478sampling variabilitythe naturally occurring variability found in samples133
10434845479levelsthe values that the experimenter used for a factor134
10434845480the four principles of experimental designcontrol, randomization, replication, and blocking135
10434845481completely randomized designa design where all experimental units have an equal chance of receiving any treatment136
10434845482interpreting p valueif the true mean/proportion of the population is (null), the probability of getting a sample mean/proportion of _____ is (p-value).137
10434845483p̂1-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
10434845484probability of getting a certain p̂1-p̂2 (ex. less than .1)plug in center and spread into bell curve, find probability139
10434845485Confidence intervals for difference in proportions formula(p̂1-p̂2) plus or minus z*(√((p1(1-p1)/n1)+(p2(1-p2)/n2))140
10434845486When do you use t and z test/intervals?t for mean z for proportions141
10434845537Significance test for difference in proportions142
10434845487What is a null hypothesis?What is being claimed. Statistical test designed to assess strength of evidence against null hypothesis. Abbreviated by Ho.143
10434845488What is an alternative hypothesis?the claim about the population that we are trying to find evidence FOR, abbreviated by Ha144
10434845489When is the alternative hypothesis one-sided?Ha less than or greater than145
10434845490When is the alternative hypothesis two-sided?Ha is not equal to146
10434845491What is a significance level?fixed value that we compare with the P-value, matter of judgement to determine if something is "statistically significant".147
10434845492What is the default significance level?α=.05148
10434845493Interpreting 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
10434845494p value ≤ αWe reject our null hypothesis. There is sufficient evidence to say that (Ha) is true.150
10434845495p value ≥ αWe fail to reject our null hypothesis. There is insufficient evidence to say that (Ho) is not true.151
10434845496reject Ho when it is actually trueType I Error152
10434845497fail to reject Ho when it is actually falseType II Error153
10434845498Power definitionprobability of rejecting Ho when it is false154
10434845499probability of Type I Errorα155
10434845500probability of Type II Error1-power156
10434845501two ways to increase powerincrease sample size/significance level α157
104348455025 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
10434845538Formula for test statistic (μ)159
10434845503Formula for test statistic (p̂) (where p represents the null)(p̂-p)/(√((p)(1-p))/n)160
10434845504probability of a Type II Error?overlap normal distribution for null and true. Find rejection line. Use normalcdf161
10434845505when do you use z tests?for proportions162
10434845506when do you use t tests?for mean (population standard deviation unknown)163
10434845507finding p value for t teststcdf(min, max, df)164
10434845508Sample 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
10434845509What 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
10434845510When doing a paired t-test, to check normality, what do you do?check the differences histogram (μ1-μ2)167
10434845511How 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
10434845512How to interpret a C% Confidence IntervalWe are C% confident that the interval (_,_) will capture the true parameter (in context).169
10434845513What conditions must be checked before constructing a confidence interval?random, normal, independent170
10434845514C% 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
10434845539What's the z interval standard error formula?172
10434845515How do you find z*?InvNorm(#)173
10434845516How 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
10434845517How 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
10434845518Finding 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
10434845519Finding the confidence interval when the standard deviation of the population is *known*x bar +/- z*(σ/√n)177
10434845520Checking normal condition for z* (population standard deviation known)starts normal or CLT178
10434845521Finding the confidence interval when the standard deviation of the population is *unknown* (which is almost always true)x bar +/- t*(Sx/√n)179
10434845522degrees of freedomn-1180
10434845523How do you find t*?InvT(area to the left, df)181
10434845524What 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
10434845525a point estimator is a statistic that...provides an estimate of a population parameter.183
10434845526Explain the two conditions when the margin of error gets smaller.Confidence level C decreases, sample size n increases184
10434845527Does 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
10434845528Sx and σx: which is which?Sx is for a sample, σx is for a population186
10434845529How do we know when do use a t* interval instead of a z interval?you are not given the population standard deviation187
10434845530Checking 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
10434845531How 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
10434845532t* 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
10434845533margin of error formulaz* or t* (standard error)191
10434845534When 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
10434845535What is it looking for if it asks for the appropriate critical value?z/t* interval193
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