AP Stat Midterm

How to calculate r

2nd-catalog-alpha- x-1 - diagnosticon, then stat-calc-linreg

tend to be strong opinions-biased, so not rep. of population (call-in polls) bad to use

voluntary response sample

-.25<r<0

weak negative linear association

0<r<.25

weak positive linear association

explanatory is the __ variable

x

symbol for means of statistic

xbar

response is the ___ variable

y

how to calcuate residuals

y-yhat

how to find y intercept

ybar-b(xbar)

does equal to matter for discrete?

yes

the distance between an observation and the mean expressed as a certain number of standard deviations; this is positive (negative) if the observation lies above (below) the mean

z-score

what does the upside-down U mean in the A and Bs?

and

lurking variable affects both x and y

common response.

lurking variable affects onlly y (response)

confounding

measureable random variable

continuous

effects of lurking variables, compare treatment and placebo (principle of experimental design)

control

selection bias (mall intercept interviews) bad to use

convenience sample

both units are quantitave

correlation

imposes treatment to observe responses

experiment

use of regression to predict outside range of explanatory variables (not always accurate, never do)

extrapolation

explanatory variables in experiments

factors

how to find normal estimation for prob __ or more outcome

find mean, standard deviation, and make sure sample size is large enough. normcdf(outcome # [lower lim], 10^99, mean, standard dev.)

How do you find relative frequency

for each count, divide by total number of data points, then convert to a percentage

Use when finding the first success on or before the nth trial (p,n)

geometcdf

either of two discrete probability distributions: The probability distribution of the number X of Bernoulli trials needed to get one success, supported on the set { 1, 2, 3, ...} The probability distribution of the number Y = X − 1 of failures before the first success, supported on the set { 0, 1, 2, 3, ... }

geometric random variable

Why doesn't equal to matter in continuous

it's area, and there is no area of a line

how do you get estimates

large random samples

law stating that a large number of items taken at random from a population will (on the average) have the population statistics

law of large numbers

a straight line that describes how a response variable changes as an explanatory variable changes

least squares regression line

symbol for size of statistic

lowecase n

not resistant to outliers

mean

resistant to outliers

median

symbol for means of parameter

mew

expected sum of 2 outcomes

mew sub x + mew sub (add means)

expected difference of 2 outcomes

mew sub x- mew sub y (subtract means)

-.75<r<-.25

moderate negative linear association

.25<r<.75

moderate positive linear association

how to find the mean of a probability distribution

multiply each value of X by each probability P(X), then add these results together

how to get prob two independent things (and)

multiply their probabilities

Relative cumulative frequency graph

ogive

symbol for proportion of parameter

p

symbol for proportion of statistic

p hat

"and" independent p(a) etc

p(A) x p(b)

p(A) + p(B)-p(a and b) =

p(a or b)

"and" not independent p(a) etc

p(a) x p(A I B)

"or" all events p(a) etc

p(a)+ p(b) - p(a and b)

"or" mutually exclusive p(a) etc

p(a)+p(b)

sampling distribution- true. describes population. fixed #, don't know value

parameter

how to find mean of statistic proportion

parameter proportion

Experimental results caused by expectations alone; any effect on behavior caused by the administration of an inert substance or condition, which is assumed to be an active agent.

placebo effect

how to find y hat

plug in x to l-s regression line

entire group of individuals we want info about

population

how to identify causation

put x in L1and y in L2. make scatterplot. make L3 log(l2). go to2nd "y="(stat pbt) and make y list L3 and graph. then make L4 log(L1). on 2nd "y=", make x L4 and y L3. if this makes a straighter line, it's power. if so do stat-calc-pwrreg then put in y= equation into "y=" and then to 2nd "y=" and make them L1 and L2 again then graph.

What unit is r

r is unitless.

how to find slope

r(sy/sx)

impersonal chance in assigning experimental units (principle of experimental design)

randomize

best way to show causation

randomized experiments

reduce chance variarion in result (principle of experimental design)

replicate

the difference between an observed value of the response variable and the value predicted by the regression line (y - y-hat)

residual

symbol for means stand. dev. of statistic

s

part of population we examine to get info

sample

union (a + b)

sample space

the set of all possible outcomes of an event

sample space S

the most effective method of displaying the relation between two quantitative variables

scatterplot

how to find binomial stand dev

square root (np(1-p))

how to find stand. dev. of statistic prop.

square root (p(1-p))/n) or sqare root (pq/n)

how to find the standard deviation of a probability distribution

square root of : sum of x^2 times p(x)-mean^2 (or square root of variance)

simple random sample

srs

whole population in hat and draw names, everyone has an equal chance

srs

sampling dist.- describes sample. value known, but can change sample to sample. estimates.

statistic

experimental groups split by similarities. sampling

stratified

-1<r<-.75

strong negative linear association

.75<r<1

strong positive linear association

how to find the variance of a probability distribution

sum[sigma] of (x^2 x p(x)^2 - mean^2)

standard deviation explanatory shorthand (sample)

sx

standard devation response shorthand

sy

how to find a high outlier

the number is higher than Q3+1.5(IQR)

how to find a low outlier

the number is lower than Q1-1.5(IQR)

levels and combinations in experiments

treatment

how to word correlation (linear regression)

a% of the variation in y can be explanws by the linear model relating x to y.

what numbers can r be

between -1 and 1

systematically favors certain outcomes (prison survey to find prop of people who commit crimes)

bias

finds AT MOST. (total number, percent, number wanted)

binomcdf

how to find prob. at most __ outcome

binomcdf ( # trials, probability, outcome wanted)

used when working with total # of trials, not srs

binomials

how to find prob. exactly __ outcome

binompdf(# of trials,probability,outcome wanted)

grouping experiment subjects by differences (male, female)

blocking

How to determine symmetry in distribution

boxplot

symbol for size for parameter

capital N

contacts every individual in population

census

As the sample size increases, the distribution of the sample mean of a randomly selected sample approaches the normal distribution.

central limit theorem

area of a density curve

1

area under density curve

1

what does cumulative relative freq. add up to

1

how to find prob __ or more outcome

1-binomcdf (# trials, prob, # to stop at or get [one less that wanted outcome number])

how to find at least one in a binomial on calculator

1-binompdf(# of trials, prob, 0)

How to find at least 1

1-p(0)

how to find prob. at least one

1-p(0), so 1-binompdf(sample, p(success), 0)

divide population into clusters

cluster sampling

simple random sample: make a list of your population, assign numbers to the list, randomly pick numbers, do not replace. unbiased

SRS

inverse cumulative probability; used to find the X value when the mean, standard deviation, and z-score are known

inverse norm

how to find inverse norm (not area of curve)

invnorm(area,mean,st.dev)

how to find z-score

(x-mean) divided by standard deviation

how to measure correlation by hand

+-(1-(length minor axis/length major axis))

how to find mean sub x

1/p

states that nearly all values lie within three standard deviations of the mean in a normal distribution

68-95-99.7 rule

how to find (pA or B) if independent

P(A) + P(B) -p(a and B)

how to find interquartile range (IQR)

Q3-Q1

percent of a whole

Relative frequency

mathematical model, always above x-axis, normal dist., area always equals one, area under curve and above any range of value equals proportion of all aobservations that fall in that range

density curve

countable random variable

discrete

mutually exclusive, can't happen at the sme time

disjoint

random events must not be dependent to other events in probability

independence

can you say explanatory variable causes the response variable

no

does equal to matter for continuous?

no

the tendency for a sample to differ from the population because measurements are not obtained from all individuals selected for inclusion in the sample

nonresponse bias

(left end point, right end point, mean, standard deviation)

normcdf

calculator function used to find the area under the standard normal curve

normcdf

what does the c mean on a and b (complementary)

not that one. 1-P(that one)

how to find binomial mean

np

how do you know if the sample size is large enough

np>/= 10 and n(1-p) >/= 10

symbol for means standard dev. of parameter

o with a ponytail

observes individual and measure variable of interest but does not attemp to influence respoense

observational study