AP Stats

Cluster sample

Sample all individuals from some of the groups

Systemic random sample

Use equal intervals until you select the amount of individuals you want

Block

A group of experimental units that are similar

Randomized block design

Separate subjects into blocks and then randomly assign treatments within each block

P( a or b)

P(a)+P(b)

P(a given b)

P(a and b)/p(b)

Divide by p of the given condition

If two events are independent

P(a)=P(a given b)=(a given the complement of b)

P(a&b)=

P(a) times P(b given a) conditional

P(a) times p(b) independent

Conditions for geometric distribution

Binary

Independent trials

Trials until success

Same p(success)

Geometric distribution center

1/p

Geometric distribution variability

SD=(Sqrt(1-p))/p

Large counts condition

n(p)>/=10

n(1-p)>/=10

Binomial distribution conditions

Binary

Independent trials

Number of trials is fixed

Same p(success)

Binomial distribution conditions

Binary

Independent trials

Number of trials is fixed

Same p(success)

When adding a constant

Shape:same

Center:add/subtract c

Variability: same

When combining random variables

Means can be added to find the combined mean

SD: sqrt(SDx squared + SDy squared)

Discrete random variable

Has a countable number of variables with gaps

Continuous random variable

Has infinite values with no gaps

To check if the sampling distribution is approx normal for p hat

Check 10% condition

Sampling distribution

The distribution of values for a statistic for all possible samples of a given size from a given population

For a confidence interval for a difference of proportions check

Independent random samples

10%

Large counts

All x2

For a confidence interval for a proportion check

Random

10%

Large counts

For a sampling distribution of xbar-xbar shape is approx normal if

pop distrs are approx normal or n is greater than or equal to 30

Central limit theorem

Sampling distribution of x bar is approx normal when the sample size is large enough ( greater than or equal to 30)

If sampling without replacement check

10% condition

Shape of x bar distribution is approx normal if

The pop distr is approx normal

For all significance tests

State hypotheses and define parameter

Test statistic =

(statistic-parameter)/standard dev

Type I error

Null is true but gets rejected

Type II error

Ha is true but we fail to reject Ho

Power is

The probability of rejecting Ho given Ha is true

Power interpretation

If Ha is true, there is a POWER probability of finding convincing evidence to make the correct decision and reject Ho (in context)

P(type I error)=

alpha

P(type II error)=

1-power

To increase the power

Increase sample size, alpha lvl, or distance to Ha

For a confidence interval for a mean check

Random

10%

Normal/large sample

Pop distr is approx norm, n>/= 30, or sample data shows no strong skew/outliers

If not on table B

Round down

For confidence interval for a difference of means check

Random: ind Rand samples or random assignment

10%

Normal/large sample

Normal/large sample

Pop distr is approx normal

n>/=30

Sample data shows no strong skews or outliers

Null hypothesis for chi square GOF

The claimed distribution of the (categorical variable) is true

Ha for chi square GOF

The claimed distribution for (categorical variable) is not true

For chi square GOF check

Random

10%

Large counts (all expected values > 5)

If chi square p value is statistically significant

Follow up analysis is needed

Follow up analysis

The largest component of chi square is ___ because the observed counts of ___ was higher/lower than expected

Chi square test for homogeneity expected counts=

(Row total times column total)/grand total

To find p value for chi square

Chi square cdf or pdf

Chi square test for homogeneity Ho

There is no difference in ___

Chi square test for homogeneity Ha

There is a difference in ___

Chi square test for independence expected count=

(Row total times column total)/grand total

Chi square test for independence Ho

There is no association between __ and __

Chi square test for independence Ha

There is an association between __ and __

If 1 sample & 1 variable

Chi square GOF

If 2+ samples & 1 variable

Chi square test for homogeneity

If 1 sample 2 variables

Chi square test for independence

In computer output a (y-int) is

Top left

In computer output b (slope) is

Bottom left

In computer output s is

SD of residuals

SEb is

SE of the slope

In computer output SEb is

Bottom second from left

SEa is

Standard deviation of y intercept

In computer output SEa is

Top second from left

For t interval for ß (slope) check

Linear: scatterplot linear & residual plot no pattern)

Independent: 10%

normal: no skew/outliers on residual dotplot

Equal SD: no sideways Xmas tree pattern on residual plot

Random: random sample or assignment

For t interval for ß df=

n-2

Formula for t interval for ß

b ± t* times SEb

For t test for slope with computer output p is located

Bottom right

For t test for slope test statistic is

(b-ß)/SEb

df for chi square homogeneity and independence

(# columns -1)(# rows -1)