| 13972861427 | How do you check if there is outliers? | calculate IQR; anything above Q3+1.5(IQR) or below Q1-1.5(IQR) is an outlier | | 0 |
| 13972861428 | If a graph is skewed, should we calculate the median or the mean? Why? | median; it is resistant to skews and outliers | | 1 |
| 13972861429 | If a graph is roughly symmetrical, should we calculate the median or the mean? Why? | mean; generally is more accurate if the data has no outliers | | 2 |
| 13972861430 | What is in the five number summary? | Minimum, Q1, Median, Q3, Maximum | | 3 |
| 13972861431 | Relationship between variance and standard deviation? | variance=(standard deviation)^2 | | 4 |
| 13972861432 | variance definition | the variance is roughly the average of the squared differences between each observation and the mean | | 5 |
| 13972861433 | standard deviation | the standard deviation is the square root of the variance | | 6 |
| 13972861434 | What should we use to measure spread if the median was calculated? | IQR | | 7 |
| 13972861435 | What should we use to measure spread if the mean was calculated? | standard deviation | | 8 |
| 13972861436 | What is the IQR? How much of the data does it represent? | Q3-Q1; 50% | | 9 |
| 13972861437 | How 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 it | | 10 |
| 13972861617 | What is the formula for standard deviation? | |  | 11 |
| 13972861438 | Categorical variables vs. Quantitative Variables | Categorical: individuals can be assigned to one of several groups or categories
Quantitative: takes numberical values | | 12 |
| 13972861439 | If a possible outlier is on the fence, is it an outlier? | No | | 13 |
| 13972861440 | Things to include when describing a distribution | Center (Mean or Median), Unusual Gaps or Outliers, Spread (Standard Deviation or IQR), Shape (Roughly Symmetric, slightly/heavily skewed left or right, bimodal, range) | | 14 |
| 13972861441 | Explain 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 |
| 13972861442 | What 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 | | 16 |
| 13972861443 | What is a density curve? | a curve that (a) is on or above the horizontal axis, and (b) has exactly an area of 1 | | 17 |
| 13972861444 | Inverse Norm | when you want to find the percentile: invNorm (area, mean, standard deviation) | | 18 |
| 13972861445 | z | (x-mean)/standard deviation | | 19 |
| 13972861446 | pth percentile | the value with p percent observations less than is | | 20 |
| 13972861447 | cumulative relative frequency graph | can be used to describe the position of an individual within a distribution or to locate a specified percentile of the distribution | | 21 |
| 13972861448 | How to find and interpret the correlation coefficient r for a scatterplot | STAT plot, scatter, L1 and L2 (Plot 1: ON); STAT --> CALC --> 8:LinReg(a+bx)
No r? --> 2nd 0 (Catalog) down to Diagnostic ON | | 22 |
| 13972861449 | r | tells us the strength of a LINEAR association. -1 to 1. Not resistant to outliers | | 23 |
| 13972861450 | r^2 | the proportion (percent) of the variation in the values of y that can be accounted for by the least squares regression line | | 24 |
| 13972861451 | residual plot | a 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 PATTERN | | 25 |
| 13972861452 | regression line | a 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 |
| 13972861453 | residual formula | residual=y-y(hat) aka observed y - predicted y | | 27 |
| 13972861454 | What 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 trial | | 28 |
| 13972861455 | What 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 trial | | 29 |
| 13972861456 | n | number of trials | | 30 |
| 13972861457 | p | probability of success | | 31 |
| 13972861458 | k | number of successes | | 32 |
| 13972861459 | Binomial Formula | |  | 33 |
| 13972861460 | Binomial Calculator Function to find P(X=k) | binompdf(n,p,k) | | 34 |
| 13972861461 | Binomial Calculator Function for P(X≤k) | binomcdf(n,p,k) | | 35 |
| 13972861462 | Binomial Calculator Function for P(X≥k) | 1-binomcdf(n,p,k-1) | | 36 |
| 13972861463 | mean of a binomial distribution | np | | 37 |
| 13972861464 | standard deviation of a binomial distribution | √(np(1-p)) | | 38 |
| 13972861465 | Geometric Formula for P(X=k) | (1-p)^(k-1) x p | | 39 |
| 13972861466 | Geometric Calculator Function to find P(X=k) | geometpdf(p,k) | | 40 |
| 13972861467 | Geometric Calculator Function for P(X≤k) | geometcdf(p,k) | | 41 |
| 13972861468 | Geometric Calculator Function for P(X≥k) | 1-geometcdf(p,k-1) | | 42 |
| 13972861469 | Mean of a geometric distribution | 1/p=expected number of trials until success | | 43 |
| 13972861470 | Standard deviation of a geometric distribution | |  | 44 |
| 13972861471 | What 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 |
| 13972861472 | how do you enter n choose k into the calculator? | type "n" on home screen, go to MATH --> PRB --> 3: ncr, type "k" | | 46 |
| 13972861473 | μ(x+y) | μx+μy | | 47 |
| 13972861474 | μ(x-y) | μx-μy | | 48 |
| 13972861475 | σ(x+y) | √(σ²x+σ²y) | | 49 |
| 13972861476 | What 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 |
| 13972861477 | What 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 |
| 13972861478 | σ(x-y) | √(σ²x+σ²y) --> you add to get the difference because variance is distance from mean and you cannot have a negative distance | | 52 |
| 13972861479 | calculate μx by hand | X1P1+X2P2+.... XKPK (SigmaXKPK) | | 53 |
| 13972861480 | calculate var(x) by hand | (X1-μx)²p(1)+(X2-μx)²p(2)+.... (Sigma(Xk-μx)²p(k)) | | 54 |
| 13972861481 | Standard deviation | square root of variance | | 55 |
| 13972861482 | discrete random variables | a fixed set of possible x values (whole numbers) | | 56 |
| 13972861483 | continuous 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 |
| 13972861484 | What 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 |
| 13972861485 | mutually exclusive | no outcomes in common | | 59 |
| 13972861486 | addition rule for mutually exclusive events
P (A U B) | P(A)+P(B) | | 60 |
| 13972861487 | complement rule
P(A^C) | 1-P(A) | | 61 |
| 13972861488 | general addition rule (not mutually exclusive)
P(A U B) | P(A)+P(B)-P(A n B) | | 62 |
| 13972861489 | intersection
P(A n B) | both A and B will occur | | 63 |
| 13972861490 | conditional probability
P (A | B) | P(A n B) / P(B) | | 64 |
| 13972861491 | independent events (how to check independence) | P(A) = P(A|B)
P(B)= P(B|A) | | 65 |
| 13972861492 | multiplication rule for independent events
P(A n B) | P(A) x P(B) | | 66 |
| 13972861493 | general multiplication rule (non-independent events)
P(A n B) | P(A) x P(B|A) | | 67 |
| 13972861494 | sample space | a list of possible outcomes | | 68 |
| 13972861495 | probability model | a description of some chance process that consists of 2 parts: a sample space S and a probability for each outcome | | 69 |
| 13972861496 | event | any collection of outcomes from some chance process, designated by a capital letter (an event is a subset of the sample space) | | 70 |
| 13972861497 | What 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 |
| 13972861498 | Complement | probability that an event does not occur | | 72 |
| 13972861499 | What is the sum of the probabilities of all possible outcomes? | 1 | | 73 |
| 13972861500 | What is the probability of two mutually exclusive events? | P(A U B)= P(A)+P(B) | | 74 |
| 13972861501 | five basic probability rules | 1. 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 |
| 13972861502 | When is a two-way table helpful | displays the sample space for probabilities involving two events more clearly | | 76 |
| 13972861503 | In statistics, what is meant by the word "or"? | could have either event or both | | 77 |
| 13972861504 | When can a Venn Diagram be helpful? | visually represents the probabilities of not mutually exclusive events | | 78 |
| 13972861505 | What 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 |
| 13972861506 | What does the intersection of two or more events mean? | both event A and event B occur | | 80 |
| 13972861507 | What does the union of two or more events mean? | either event A or event B (or both) occurs | | 81 |
| 13972861508 | What 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 outcome | | 82 |
| 13972861509 | the 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 repetitions | | 83 |
| 13972861510 | How do you interpret a probability? | We interpret probability to represent the most accurate results if we did an infinite amount of trials | | 84 |
| 13972861511 | What 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 outcome | | 85 |
| 13972861512 | simulation | the imitation of chance behavior, based on a model that accurately reflects the situation | | 86 |
| 13972861513 | Name and describe the four steps in performing a simulation | 1. 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 interest | | 87 |
| 13972861514 | What 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 simulation | | 88 |
| 13972861515 | What does the intersection of two or more events mean? | both event A and event B occur | | 89 |
| 13972861516 | sample | The part of the population from which we actually collect information. We use information from a sample to draw conclusions about the entire population | | 90 |
| 13972861517 | population | In a statistical study, this is the entire group of individuals about which we want information | | 91 |
| 13972861518 | sample survey | A 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 |
| 13972861519 | convenience sample | A sample selected by taking the members of the population that are easiest to reach; particularly prone to large bias. | | 93 |
| 13972861520 | bias | The design of a statistical study shows ______ if it systematically favors certain outcomes. | | 94 |
| 13972861521 | voluntary response sample | People decide whether to join a sample based on an open invitation; particularly prone to large bias. | | 95 |
| 13972861522 | random sampling | The use of chance to select a sample; is the central principle of statistical sampling. | | 96 |
| 13972861523 | simple random sample (SRS) | every set of n individuals has an equal chance to be the sample actually selected | | 97 |
| 13972861524 | strata | Groups of individuals in a population that are similar in some way that might affect their responses. | | 98 |
| 13972861525 | stratified random sample | To 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 |
| 13972861526 | cluster sample | To 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 |
| 13972861527 | inference | Drawing conclusions that go beyond the data at hand. | | 101 |
| 13972861528 | margin of error | Tells how close the estimate tends to be to the unknown parameter in repeated random sampling. | | 102 |
| 13972861529 | sampling frame | The list from which a sample is actually chosen. | | 103 |
| 13972861530 | undercoverage | Occurs when some members of the population are left out of the sampling frame; a type of sampling error. | | 104 |
| 13972861531 | nonresponse | Occurs when a selected individual cannot be contacted or refuses to cooperate; an example of a nonsampling error. | | 105 |
| 13972861532 | wording of questions | The 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 |
| 13972861533 | observational study | Observes individuals and measures variables of interest but does not attempt to influence the responses. | | 107 |
| 13972861534 | experiment | Deliberately imposes some treatment on individuals to measure their responses. | | 108 |
| 13972861535 | explanatory variable | A variable that helps explain or influences changes in a response variable. | | 109 |
| 13972861536 | response variable | A variable that measures an outcome of a study. | | 110 |
| 13972861537 | lurking variable | a variable that is not among the explanatory or response variables in a study but that may influence the response variable. | | 111 |
| 13972861538 | treatment | A 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 |
| 13972861539 | experimental unit | the smallest collection of individuals to which treatments are applied. | | 113 |
| 13972861540 | subjects | Experimental units that are human beings. | | 114 |
| 13972861541 | factors | the explanatory variables in an experiment are often called this | | 115 |
| 13972861542 | random assignment | An 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 |
| 13972861543 | replication | An 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 |
| 13972861544 | double-blind | An experiment in which neither the subjects nor those who interact with them and measure the response variable know which treatment a subject received. | | 118 |
| 13972861545 | single-blind | An 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 |
| 13972861546 | placebo | an inactive (fake) treatment | | 120 |
| 13972861547 | placebo effect | Describes the fact that some subjects respond favorably to any treatment, even an inactive one | | 121 |
| 13972861548 | block | A 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 |
| 13972861549 | inference about the population | Using 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 |
| 13972861550 | inference about cause and effect | Using 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 |
| 13972861551 | lack of realism | When 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 |
| 13972861552 | institutional review board | A 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 |
| 13972861553 | informed consent | A 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 |
| 13972861554 | simulation | a model of random events | | 128 |
| 13972861555 | census | a sample that includes the entire population | | 129 |
| 13972861556 | population parameter | a number that measures a characteristic of a population | | 130 |
| 13972861557 | systematic sample | every fifth individual, for example, is chosen | | 131 |
| 13972861558 | multistage sample | a sampling design where several sampling methods are combined | | 132 |
| 13972861559 | sampling variability | the naturally occurring variability found in samples | | 133 |
| 13972861560 | levels | the values that the experimenter used for a factor | | 134 |
| 13972861561 | the four principles of experimental design | control, randomization, replication, and blocking | | 135 |
| 13972861562 | completely randomized design | a design where all experimental units have an equal chance of receiving any treatment | | 136 |
| 13972861563 | interpreting p value | if the true mean/proportion of the population is (null), the probability of getting a sample mean/proportion of _____ is (p-value). | | 137 |
| 13972861564 | p̂1-p̂2 center, shape, and spread | center: 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 |
| 13972861565 | probability of getting a certain p̂1-p̂2 (ex. less than .1) | plug in center and spread into bell curve, find probability | | 139 |
| 13972861566 | Confidence intervals for difference in proportions formula | (p̂1-p̂2) plus or minus z*(√((p1(1-p1)/n1)+(p2(1-p2)/n2)) | | 140 |
| 13972861567 | When do you use t and z test/intervals? | t for mean
z for proportions | | 141 |
| 13972861572 | What is a significance level? | fixed value that we compare with the P-value, matter of judgement to determine if something is "statistically significant". | | 142 |
| 13972861573 | What is the default significance level? | α=.05 | | 143 |
| 13972861574 | Interpreting the p-value | if the true mean/proportion of the population is (null), the probability of getting a sample mean/proportion of _____ is (p-value). | | 144 |
| 13972861575 | p value ≤ α | We reject our null hypothesis. There is sufficient evidence to say that (Ha) is true. | | 145 |
| 13972861576 | p value ≥ α | We fail to reject our null hypothesis. There is insufficient evidence to say that (Ho) is not true. | | 146 |
| 13972861577 | reject Ho when it is actually true | Type I Error | | 147 |
| 13972861578 | fail to reject Ho when it is actually false | Type II Error | | 148 |
| 13972861579 | Power definition | 1 - β | | 149 |
| 13972861580 | probability of Type I Error | α | | 150 |
| 13972861581 | probability of Type II Error | 1-power | | 151 |
| 13972861582 | two ways to increase power | increase sample size/significance level α | | 152 |
| 13972861583 | 5 step process: z/t test | State --> 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 Ho | | 153 |
| 13972861619 | Formula for test statistic (μ) | |  | 154 |
| 13972861584 | Formula for test statistic (p̂) (where p represents the null) | (p̂-p)/(√((p)(1-p))/n) | | 155 |
| 13972861585 | probability of a Type II Error? | overlap normal distribution for null and true. Find rejection line. Use normalcdf | | 156 |
| 13972861586 | when do you use z tests? | for proportions | | 157 |
| 13972861587 | when do you use t tests? | for mean (population standard deviation unknown) | | 158 |
| 13972861588 | finding p value for t tests | tcdf(min, max, df) | | 159 |
| 13972861589 | Sample paired t test | state--> 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 conclusion | | 160 |
| 13972861590 | What 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 chance | | 161 |
| 13972861591 | When doing a paired t-test, to check normality, what do you do? | check the differences histogram (μ1-μ2) | | 162 |
| 13972861592 | How to interpret a C% Confidence Level | In C% of all possible samples of size n, we will construct an interval that captures the true parameter (in context). | | 163 |
| 13972861593 | How to interpret a C% Confidence Interval | We are C% confident that the interval (_,_) will capture the true parameter (in context). | | 164 |
| 13972861594 | What conditions must be checked before constructing a confidence interval? | random, normal, independent | | 165 |
| 13972861595 | C% confidence intervals of sample proportions, 5 step process | State: 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). | | 166 |
| 13972861620 | What's the z interval standard error formula? | |  | 167 |
| 13972861596 | How do you find z*? | InvNorm(#) | | 168 |
| 13972861597 | How 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) | | 169 |
| 13972861598 | How 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 ends | | 170 |
| 13972861599 | Finding 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=.5 | | 171 |
| 13972861600 | Finding the confidence interval when the standard deviation of the population is *known* | x bar +/- z*(σ/√n) | | 172 |
| 13972861601 | Checking normal condition for z* (population standard deviation known) | starts normal or CLT | | 173 |
| 13972861602 | Finding the confidence interval when the standard deviation of the population is *unknown* (which is almost always true) | x bar +/- t*(Sx/√n) | | 174 |
| 13972861603 | degrees of freedom | n-1 | | 175 |
| 13972861604 | How do you find t*? | InvT(area to the left, df) | | 176 |
| 13972861605 | What 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) | | 177 |
| 13972861606 | a point estimator is a statistic that... | provides an estimate of a population parameter. | | 178 |
| 13972861607 | Explain the two conditions when the margin of error gets smaller. | Confidence level C decreases, sample size n increases | | 179 |
| 13972861608 | Does 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 parameter | | 180 |
| 13972861609 | Sx and σx: which is which? | Sx is for a sample, σx is for a population | | 181 |
| 13972861610 | How do we know when do use a t* interval instead of a z interval? | you are not given the population standard deviation | | 182 |
| 13972861611 | Checking 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) | | 183 |
| 13972861612 | How to check if a distribution is normal for t*, population n<15 | plug data into List 1, look at histogram. Conclude with "The histogram looks roughly symmetric, so we should be safe to use the t distribution) | | 184 |
| 13972861613 | t* confidence interval, 5 step process | State: 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). | | 185 |
| 13972861614 | margin of error formula | z* or t* (standard error) | | 186 |
| 13972861615 | When 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 given | | 187 |
| 13972861616 | What is it looking for if it asks for the appropriate critical value? | z/t* | | 188 |
