HW assignment Day 22
For Monday: Reading: 4.1, 2, 3. We'll do 4.1, 2,
3. Skip 4.4 and Skip Ch. 5.
| Postpone all
Probability: Sec. 4.1 p. 215, 4.1, 2, 3 parameter/statistic 4.9 3 of a kind
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Read, to discuss
Postpone p. 218 4.6 random digits
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Optional
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Ch. 4, Probability and Sampling Distributions.
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: Individual
sets of 25 showed 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. 4.1:
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
Sample median
Pop. median
Sample proportion p-hat Pop.
proportion p
Sample line height y-hat Pop.
regression line height y
The actual value of the Statistic will vary,
depending on the particular sample. "Sampling variability"
The Statistic "estimates" 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.
Some examples of statistics:
Height: U.S. young
women: pop. mean= 64.5", pop. s.d. 2.5"
(text p.66. Caveat: rounded?)
Math 151, Spring '01, xbar = 64.2,
s = 3.75.
Fall '01, xbar = 65.01, s = 3.22.
Spring '02, xbar = 64.53, s = 2.91.
Fall '02, xbar = 63.89, s = 2.48.
Spring '03, xbar = 64.98, s = 3.29
Spring '04, xbar = 65.33, s = 2.25
Coin flip: Proportion
of heads p = 1/2
(?)
p-hat = 256/520 = .492 (combined data from many
past classes)
Thumbtack: Proportion
of point-up p =
(??)
p-hat = 441/691 = .6382 (one past class, Math
251)
Spinning
penny From p. 216, #4.4,
Each of you took a sample of size 50 from the population of all possible
penny spins, got a statistic, p-hat.
Add
YOUR result to the list going around.
Also tell whether you FLICKED or TWIRLED the penny.
Results
so far from spinning penny
' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' '
' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' '
' ' ' ' ' ' ' ' ' ' ' '
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" here is more general--pattern
is not necessarily equally likely
Prof. Persi Diaconis (a table magician) can flip
a coin so precisely it always comes up the way he wants. His
coinflipping
is not a random phenomenon. Mine is.
"Probability" of particular something
happening:
proportion of times it would happen in a very long
series of independent
repetitions of the phenomenon.
(independence:
outcome of one trial (repetition) must not influence the outcome of any
other.)
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