ap stats final test review

what is a quantitative variable

a numerical value

what is a categorical variable

variable that takes on groups and labels

what is association

when knowing the value of one variable helps to predic the value of the other variable

if theres no association on a bar graph, what should it look like

all bars are the same length

what are the features of misleading graphs?/

the axis doesn't start at 0

theres an image in a bar graph

what is a side by side bar graph

a graph where each bar represents the frequency or relative frequency for each group

what is a segmented bar graph

graph where bars are staced to make 100%

what is a mosiac plot

a segmented bar graph where the bar width is proportional to the group size

what does a symmetric graph look like

what does a skewed left graph look like

what does a skewed right graph look like

how do you describe a distrubution?

Shape

Outliers

Center

Variability

*make sure to use context

if the distribution is skewed we use the ________ as the center and the ______ to measure the variability

median, IQR

if the distribution is symmetric we use the ________ as the center and the ______ to measure the variability

mean, standard deviation

how do you calculate the range

max-min

what is standard deviation

how much the data typically varies from the mean

is the median resistant to outliers?

yes, its not greatly effected by outliers

are the mean/standard deviation resistant to outliers?

no, greatly effected by outliers

how do you calculate a low outlier?

Q1-1.5 x IQR

how do you calc. a high outlier?

Q3+1.5 x IQR

what is included in the 5 number summary?

minimum, Q1, median, Q3, maximum

how are outliers displayed in a modified box plot?

*

what is a percentile (relative cummalative frequency)

the percent of data values less than or equal to a given value

what is an ogive

a graph that represents the cumulative frequency or cumulative relative frequency for the class

in an ogive, which percentiles do the Q1, med, and Q3 represent

Q1= 25%

med=50%

Q3=75%

how do you calculate a z score

what does a z score tell us?

how many standard deviations above or below teh mean a data value is

how does the shape of linear data change with +/- of a constant

stays same

how does the shape of linear data change with multiplication/division of a constant

stays the same

how does the center of linear data change with +/- of a constant

+/- by the constant

how does the center of linear data change with multiplication/division of a constant

multiply/divide by the constant

how does the variability of linear data change with +/- of a constant

stays the same

how does the center of variability data change with multiplication/division of a constant

multiply/divide by the constant

what is the total area of a density curve

1

what does a uniform curve look like

what is the empirical rule

if a distribution is approx. normal:

what is an explanatory variable

(x variable) used to predict/explain

what is a response variable

(y variable) outcomes of the study/experiment

how do you describe a scatterplot?

D: direction (+/-)

U: unusual features (odd points, gaps, clusters)

F: form (linear/non linear)

S strength (weak, moderate, strong) correlation

*context

what is correlation (r)

tells you the direction and strength of the linear relationship

interpret correlation (r)

the linear relationship between (x) + (y) is (strength) and (direction).

interpret coefficient of determination (r^2)

the percent of variation in (y) can be explained by the linear relationship with (x). *closer to 1/100% is good)

interpret y-int

when (x=0), the predicted (y) is (y-int)

interpret slope

for each additional (x) the predicted (y) increases/decreases by (slope)

how do you calculate a residual

actual-predicted

interpret residual

the actual (y) is (residual) below/above the predicted value

what is extrapolation

predicting data beyond the measured points

what does LSRL stand for and what does it do

least squares regression line; minimizes the sum of the squared residuals

what characteristics do you want in a residual plot?

- no pattern

- x values and residuals

how do outliers effect linear data sets?

horizontal: tilt the line

vertical: moves line up or down

what is a high leverage point

have large or small x values and horizontal outliers

what is an influential point

when removing the point changes the LSRL

describe how to perform a SRS

1) label (assign numbers)

2) randomize (random # generator)

3) select (find the things that correspond to the #'s)

what is a stratified random sample

a sample where we split the population into groups (strata) and take the SRS from each group

*each strata has individuals with similar characteristics

*must stratify ona variable that will effect responses

a good sampling method is....

-unbiased

-low variability

what is a cluster sample

sampling all from SOME groups

what is a systematic sample

choosing random starting points and systematically taking objects at certain # apart

"every 8th person"

what is undercoverage

when some members of population can't be included in the sample

what is nonresponse bias

whena an indivual chosen for a sample doesn't respond or can't be reached

what is response bias

bias in the wording of a question

-interviewer bias

-people lying

what is an observational study

using or observing data already collected, no treatments are imposed.

what is an experiment

impacts treatments and allows u to establish cause and effect

what is a confounding variable

an outside variable that could influence the explanatory and response variables

what are experimental units

the people (subjects) or things (units) the experiment is performed on

what is a treatment

what is done to the units/subjects

*determined by explanatory variable

describe an experiment

1) random assignment

2) replication: more than 1 in each group

3) comparison: 2+ treatments

4) control: other variables stay the same

describe random assignment

1) label

2) randomize

3) assign

* shows causation and minimizes confounding variables

what is placeabo effect

when a fake treatment appears to work

what is a randomized block design

separate the subjects into blocks, then randomly assign to treatments in each block

-block ona characteristic that can impact results

what is a matched pairs design

the subjects are paired up and randomly assigned to treatments

-each subject recieves each treatments in a diff. order

what does statistically significant mean

when results of a study are too unusual to happen by chance alone

*5%

what is the law of large numbers

if we do something many times, the proportion will approach the true probablity

what is a simulation

imitation of chance behavior based on a model that accurately reflects the situation

describe a simulation process

1) describe how you will simulate one trial

2) perform many trials

3) use the results to answer the question

what is a compliment

the probability of an eent NOT happening

what is the probability of a compliment

1-P(A)

what are mutually exclusive events (disjoint)

events that can't happen at the same time

if mutually exclusive:

P(A or B) = P(A)+P(B)

what is a probability model

lists all possible outcomes and their probabilites

-probabilites must add to 1

-all probabilities between 0-1

what is the general addition rule

what is conditional probability

P(A/B) "probability of A given B"

-look at a specific row or column in table

what does it mean to be independent

when knowing one event has or has not occured does not affect the probability of the second event

if:

P(A)= P(A/B) = P(A/complliment of B)

then: A and B are independent

what is the general multiplication rule

P( A and B ) = P(A) P(B/A)

This is NOT on the formula sheet.

how do you calculate the P(at least one)

1-P(none)

what is a discrete random variable

fixed number of values with gaps in between

how do you "add" standard deviaiton

add the VARIENCES (SD^2+ SD^2)

how do you know if something is binomial

B: binary- success and failure

I: independent trials

N: number of trials (FIXED)

S: same probability of success

*binomcdf(n,p,k)

n=number of trials

p=probability of success

k=number of successes

how do u calculate mean and SD for binomial dist.

mean= n times p

SD= sqrt (n times p) (1-p)

what are the conditions for a geometric distriution:

B: binary

I: independent

T: trials til success

S: same probability of success

what is parameter

a number that describes a population

what is a statistic

a number that describes a sample

what is a sampleing distribution

the dist. of values of a statistic for all possible samples of a given size from the population

as sample size increases, variability ____

decreases

what is a point estimate

a statistic that provides a reasonable estimate for the population parameter

interpret confidencelevel

if we take many many samples of the same size, and calculate confidence intervals about __% of them will capture the true (parameter in context).

what are the conditions for a confidence interval for p

1) random

2) n<10% of pop.

3) approx. normal (n times p)

what is the 4 step process for population proportion

state: parameter and confidence level

plan: name procedure,conditions

do: p hat +/- Z* times (standard error)

if you don't know p hat, use what value?

.5

4 step process for confidence interval for p1-p2

state: true diffeence in proportions

plan: 2 sample z interval for p and conditions

do: p1-p2 +/- Z* (formula sheet)

what is null hypohesis (ho)

assuned true by default

alternative hypothesis (ha)

what you are trying to prove