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Chapter 7- AP Statistics
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Terms in this set (21)
Statistic (*S*tatistic=
S
S
tistic (*S*tatistic=*S*ample)
A number that describes some characteristic of a SAMPLE
Parameter (*P*arameter=
P
P
ameter (*P*arameter=*P*opulation
A number that describes some characteristic of the POPULATION
Sampling distribution
The distribution of values taken by the statistic in all possible samples of the same size from the same population
Standard deviation of a sampling distribution
sqrt[(p(1-p))/n]
Standard deviation of a sampling distribution of the mean
standard deviation/sq(n)
CLT
Draw an SRS of size n from any population with mean x and finite standard deviation.
When n is large, the sampling distribution of sample mean x is approximately Normal
The sampling distribution of mean x has standard deviation (standard deviation/sqrt(x), even if the population is?
Not Normally distributed
When n is large, the sampling distribution of mean x is approximately Normal, even if the population is?
Not Normally distributed
The population distribution and the distribution of sample data describe?
Individuals
A sampling distribution describes how a statistic?
Varies in many samples from the population
Unbiased estimator
A statistic used to estimate a parameter if the mean of its sampling distribution is equal to the true value of the parameter being estimated. Its value will sometimes exceed the true value of the parameter and sometimes be less if too many samples are taken. There is no tendency to over/under estimate the parameter. "no favoritism"
Biased estimator
The center of the sampling distribution for a statistic is much less than the corresponding parameter value.
How do you get a trustworthy estimate of an unknown population parameter?
Use an unbiased estimator (but doesn't guarantee that the value of your statistic will be close to the actual parameter value)
Variability of a statistic
Described by the spread of its sampling distribution. This spread is determined by the size of the random sample. Larger samples give smaller spread. The spread does not depend on the size of the population, as long as the population is at least 10x the sample.
Does taking a large sample fix bias?
No
What is the ideal estimate?
Unbiased (accurate) and have low variability (precise)
The standard deviation gets smaller as n gets?
Larger
The value of standard deviation p^ depends on?
p and n
The values of the mean x are less spread out for what size samples?
Larger
The shape of the distribution of mean x depends on the shape of the?
Population distribution
If the population distribution is Normal, then so is the?
Sampling distribution of mean x (no matter what the sample size is)
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