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AP Stats

Terms in this set (57)

population vs. sample
the population is the whole group while a sample are parts of the population.
census
study of everything in a population.
simple random sample
sample in which every group of a given size has an equal chance of being chosen
stratified sampling
- population is divided into strata, based on similar characteristic
- SRS within each stratum is taken
cluster random sample
- population is divided into clusters of individuals that are near one another
- SRS of clusters is taken
- all individuals within each cluster are sampled
systematic random sample
randomly choose a start point, then sample at a fixed periodic interval
bias
a systematic tendency to favor certain responses over others
variance
the square of the standard deviation, it is a description of how much each score varies from the mean.
under-coverage bias
when some members of the population are less likely to be chosen or cannot be chosen in a sample.
nonresponse bias
when an individual chosen for the sample can't be contacted or refuses to participate.
response bias
when there is a systematic pattern of inaccurate answers to a survey question.
How does increasing sample size impact Bias? Variance?
Bias:
Unaffected

Variance:
Decreases
sampling variability
how much an estimate varies between samples
z score
a measure of how many standard deviations you are away from the mean
empirical rule
68/95/99.7
mean
sum of all the data values divided by the number of values
central limit theorem
when sample size n is large, the sampling distribution of the sample mean x is approximately normal
median
middle value of an ordered data set
Q1
median of the first half of the ordered data set
Q3
median of the second half of the ordered data set
IQR
Q3 - Q1
standard deviation
typical distance that each value is away from the mean
outlier
1.5 * IQR below the Q1 and above Q3
percentile
the percent of data values less than or equal to a given value
correlation coeffecient (r)
gives the direction and quantifies the strength of a linear relationship
residual
observed y - predicted y
residual plot
apparent randomness = good sign
patterns = bad sign
coefficient of determination (r^2)
the percent of variation in the response variable that is explained by the explanatory variable in the model
s
measures the typical distance btwn the actual y-values and the predicted y-values
observational study
- taken w/o imposing treatments on individuals
- cannot infer cause and effect
voluntary response bias
Occurs when an invitation is sent to all individuals in population to participate. Those who choose to participate (volunteers) may differ from individuals who don't choose to participate.
confounding variable
another variable related to explanatory variable and influences response variable & may create a false perception of association btwn the two
random assignment
allows us to conclude that very large observed changes are not merely by chance
mutually exclusive
when two events have no outcomes in common - P(A and B) = 0
P(A|B)
probability of A given B
adding or subtracting constant c
- adds or subtracts c to center and location
- does not change measures of variability
- does not change shape
multiplying by constant c
- multiplies measures of center and location by c
- multiplies measures of variability by c
- does not change shape
binomial setting
arises when we perform n independent trials of the same chance process and count the # of times that a particular outcomes occurs
geometric setting
when we perform independent trails of the same chance process and record the number of trails it takes to get one success (every geometric distribution is skewed to the right)
confidence level C
in C% of all possible samples, the interval computed will capture the true parameter value
How does decreasing margin of error affect confidence level and sample size?
confidence level decreases + sample size n increases
Conditions when using confidence intervals/hypothesis tests for population proportions/means?
- random condition
- large counts condition: np > 10 and n(1-p) > 10
- 10% condition: n < 0.1N
p-value
the probability of getting evidence for the alternative hypotheses H(alternative) as strong or stronger than observed evidence when the null hypotheses H(null) is true
type I error
occurs if a test rejects H(null) when H(null) is true
type II error
occurs if a test fails to reject H(null) when H(alternative) is true
power
1 - P(type II error)
significance level
P(type I error)
increasing power of a significance test
- sample size n is larger
- significance level is larger
- null and alternative parameter values are further apart
expected count
np
chi-squared test statistic
measure of how far the observed counts are from the expected counts
Conditions when using chi-square test?
- random sample
- 10%: n < 0.10N
- large counts: all expected counts are at least 5
expected count (two-way table)
(row total * column total)/(table total)
chi-square test for homogeneity
2 samples, 2 variables
chi-square test for independence
1 sample, 2 variables
population regression line
a regression line calculated from every value in the population
conditions for regression inference
LINER: Linear, Independent, Normal, Equal SD, Random
least squares regression line
a linear model that minimizes the sum of the squared residuals
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