AP Stats all concepts Flashcards by Riya Patel

1.5 IQR rule

Low outliers < Q1-1.5 (IQR)
High outliers > Q3+1.5(IQR)

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Interpret slope

As the (x-variable) increases by 1 (unit), the predicted (y-variable)increases/decreases by (slope units).

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Interpret Y-intercept

When the (x-variable) is 0 (units), the predicted (y-variable) is (y-intercept units).

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Interpret the mean:

If many, many (context) are randomly selected, the average (context) will be about (mean value).

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Interpret standard deviation

The (context) typically vary from the (mean value) by about (standard deviation value).

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Interpret Confidence Interval (Conclusion):

We are (confidence level%) confident that the true (parameter in context) is
between (lower bound and upper bound in context.)

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Interpret Confidence Level:

l: If we constructed many, many confidence intervals from random samples of size (n), about
(confidence level%) of the intervals would capture the true (population parameter in context).

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Interpret the p-value:

Assuming the (H0 in context) is true, there is a (p-value%) chance of getting a sample (proportion/mean) of
(sample value) or something more extreme by chance in random samples of size (n).

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Interpret the power:

If the true (population parameter in context) is (Ha), there is a (power%) probability of finding convincing
evidence to reject (H0 in context).

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Describing/Comparing Distributions

Center: compare the median or mean
Shape: describe the distibution, peaks, symmetrical, bimodal, or skewed
Unusual features- gaps ro outliers
Spread- SD or range

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Resistance

IF extreme values have an impact
median is resistant
mean, range, and SD is not

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mean & Median in roughly symmetric distributions

mean=median

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Mean & median in skewed to the left distributions

mean < median

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Mean & Median in skewed to the right distributions

mean > median

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z score formula

value- mean/ SD

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Transforming Data - Addition & Multiplication

Addition= center & location are affected (mean, 5# summaries, and percentiles)
Mutiplying- center, location, variability

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what is the empirical rule

68% of the data falls under 1 standard deviation away from the mean

95% of the data falls under 2 standard deviations away from the mean

99.7% of the data falls under 3 standard deviations away from the mean

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Explaining correlation

There is a (strength- strong or weak, direction- negative or positive, form- linear or curved form) relationship between (context)

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Define extrapolation

using the line for x-values outside for the interval which is not accurate

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Define residual

y-y(hat) = actual value - predicted value

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Interpretation- residual

(actual y -variable) is less than/ greater than/ equal to than the (y-variable) predicted by the regression line with x=(context of x-variable)

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Standard deviation of regression line interpretation

The actual (y-variable) is typically about (standard deviation) away from the (y-variable) predicted by the least-square regression line x= (x-variable).

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Coefficient of Determination interpretation (r^2)

About (r^)% of the variability in the (y-variable with context) is accounted for by the least squares regression line with x= (x-variable)

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Simple random sampling define

size n chosen with equal chance of being selected

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Pros of SRS

unbiased- equal chance and easy

Cons of SRS

Issue of undercoverage- one type of factor may have more people

Stratified sampling description

Divide the population into groups (strata) based on a similar characteristic, then use an SRS to choose from EACH group

Stratified Pros

More precise than an SRS and can be cheaper if the groups are already available

Stratified cons

Difficult to divide into groups, more complex than SRS, and must have known population

Cluster sampling description

Divide the population into groups (usually by location), randomly select a group and sample everything in THAT group

Pros of cluster sampling

Cost is reduced, is unbiased, and don’t need to know entire population

Cluster sampling cons

Sample may not be representative of overall population

Systematic sampling description

Use a system (every nth number) after choosing randomly where to begin

Systematic random sampling pros

Unbiased, the sample is evenly distributed across the population, and don’t need to know entire population

Systematic Sampling cons

Large variation and can be affected by trends

Bad sampling procedures

Voluntary sampling and convenience sampling, but both are highly unrepresentative

Nonresponse bias

not willing to participate in sample

response bias

false/incorrect answers

Confounding

multiple variables and it is difficult to distinguish which variable has an effect

randomized block design description

sample is separated into two groups, then they get randomly assigned and then they are split up and one group gets a treatment and other does not

sampling variability define

samples may be different from population

matched pairs design

subjects are grouped into pairs and then between those pairs one gets a treatment; in some cases you can give two treatmets

Complementary rule for independent events

P(Ac)=1-P(A)

define mutually exclusive

no outcomes in common and can never be together

Mutually exclusive addition rule

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

General Addition Rule for Dependent Events

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

Conditional Probability equation

P(A|B)= P(A & B)/P(B)= P(both events together)/P(given event)

General Multiplication Rule

P(A and B)= P(A) * P(B)

What makes a probability model valid?

Probabilities add up to 1 All probabilities are between 0 and 1

Binomial Probability Conditions

1. Binary- successes or failures 2. Independent- 3. Number- # of tirals 4. Same probability- for each outcome

binompdf

p(x=k)

binomialcdf

p(X less than or equal to k)

how do you find a binomial/geometric probability when it states at least k

1- binomial P less than or equal to J

Defining a Binomial Distribution

Random variable____ has a binomial distribution with n= # and p=#

Defining a geometric distribution

Random Variable ____ had a geometric distribution with p= #

Checking for independent events

P(A|B)= P(A|Bc)= P(A)

Significance Rule

< 5%= statistically significant >5%= not statistically significant

Unbiased estimator

statistic of sample= match the population

sample variability for sample proportion

SD is larger for values of p closer to 0.5 SD is smaller for values of p closer to 0 or 1

Point estimate

adding interval/2

Margin of Error

subtracting interval/2 or Subtracting the larger number of the interval by the point estimate

Impacts of margin or error on confidence level and sample sizes

Decreasing margin or error= decreasing confidence level Sample sizes increase= reduces margin of Error ME= 1/sqrrt n e.g. n=4 ME= 1/2

Type 1 Error

the test finds convincing evidence that Ha is true when it isn't Reject H0 but Ho is true

Type 2 error

the test doesn't find convincing evidence that Ha is true when it really is Ha True but fail to reject H0

Effect on Type 1 Error and Type 2 error when Significance level is decreased

Type 1 error decreases but Type 2 error increases

Effect of Type 1 error and Type 2 when significance level is increased

Type 1 error increases but Type 2 error is decreased

what do you do if there is a two sided z test?

multiply the p value by 2

What effect does a large power have on the Type 2 error and Type 1 error?

Type 2 error: decreases it Type 1 error: increases

What effect does sample size, n, and significance level has on the power?

Directly proportionally N and significance level are large= power is large N and significance level small= power is small

What effects does a small power have on the Type 2 error and Type 1 error?

Type 2 error: increases it Type 1 error: decreases it