| Hand in: Sec. 3.3 p. 225ff.
3.66 bias/variability
3.71 b,c (sample means for Workers) This file is not in SPSS form, though it is in Text form (Appendix folder). Too big?? So skip part a. 3.73 Applet coin flips. Take 5 samples, not 50, for each of parts a and b, and we'll pool them next time. Do a dotplot instead of a histogram since you have so few points. 3.77 CSDATA (SPSS) Do with the Handout. Find the means for each of your 5 samples, and hand in the means in a dotplot, the 6 histograms (1 population, 5 samples.), and comments. Review: p. 247ff
|
Read, discuss
3.69 states p. 247ff
|
Optional |
How to take an SRS using SPSS--Handout
3.4, Toward Statistical Inference.
Chance behavior (a random phenomenon):
Unpredictable
in the short run, predictable regular pattern in the long run.
(Random numbers: equally
likely in the long run. "Random" in this chapter is more general--pattern
is not necessarily equally likely)
25 digits from the random number table (overhead): Individual
sets of 25 show much variability.
Pooled
shows more "flatness" --but still much variability. You would be
right to be skeptical when I told you that your "pick-a-number" choices
were not random, on the basis of just this class's data.
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
~ ~
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.
Sec. 3.4
Sample Chosen
from a Population
(varies)
(fixed, but usually unknown)
Calculate
Numerical summary: Statistic
(Latin)
Parameter(Greek
letter)
Examples:
Sample mean xbar Population
mean mu (µ)
Sample st. dev. s Pop.
standard dev. sigma
etc.
Sampling distribution of a statistic:
If we could repeat the sampling process, distribution of values for that
statistic calculated from "all possible" samples (of the given size.)
Assumes
probability sampling or randomized experiment design.
Shape, center, spread.
Shape: mound-shape, often normal; wouldn't want bimodal
or outliers.
Center of sampling distribution should be close to parameter
value:
systematically "under-or over-estimates" =
"biased estimator"
Spread (Variability): Want "tight" (around parameter value!)
--SRS produces unbiased estimators for most common statistics.
--Larger (random) sample produces less variability (spread)
Size of sample
matters, not proportion of population (as long as population is at
least 10 times sample size).
Random sampling will allow us to do inferential statistics:
How far off are we likely to be from the parameter value = Margin
of error.
How plausible is a claim based on the data (significance level)
Next: Looking at the sampling distributions we generate; then Ch. 4,
Ch. 5...
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