Sec. 3.4:
We know that a sample from a
population will not exactly represent the population. If we
take a random sample, the behavior of samples will not be
individually predictable, but there will be predictable pattern
in many random samples from the same population. Knowing the
pattern will be as good as we can do.
Population
Choose from it a Sample
(varies)
Calculate
Numerical summary:
Parameter(Greek
letter) Statistic
(Latin)
Examples:
Population mean mu
Sample mean xbar
Pop. standard dev. sigma
Sample st. dev. s
Pop. median
Sample median
Pop. proportion p
Sample proportion p-hat
etcetera.
The actual value of the Statistic will vary,
depending on the particular sample. "Sampling variability"
The Statistic "estimates" the Parameter.
(is an "estimator" of the parameter) We hope it is close to the
parameter. If we choose simple random samples, we can understand
the pattern of values the statistic can take.
Sampling distribution of statistic: Distribution
of values of the statistic from all possible samples (of size n).
Variability of statistic:
spread of its distribution.
Dependent
ONLY on sample size, not pop. size (as long as population is at least 10
times sample size)
Variance times (N-n)/(N-1), where N is pop. size
As
sample size increases, variability decreases.
Bias of statistic: An
estimator is unbiased if the mean of its sampling distribution =
the parameter we're estimating.
Read 3.4 (toward inference)
| Hand in (Monday) : 3.51, 52, 53, 54 parameter/statistic
3.55 bias and variability 3.56, 57, 58 sample size & variability 3.59 a and 3.60 a--repeat each one a total of 3 times
|
Read, discuss
|
Optional |
| Sievers home | Math251-Fall01/DayP17.htm | 10/10/01 |