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(All D&V) Ch. 19p. 366 ff 3, 4 Conditions 16 Local news ME, C, n pp. 356-7, 361-3. Problems p. 368 7, 8 Relationships 23 Deer ticks 25 Graduation The answers in the back use the 25% as the p to plug in. Redo part a (only) using 50% as the p (what you would do if you had no idea what p would be.). How many subjects do you "save" by using the 25%? 26 Hiring 28 Hiring again 29 Pilot study |
Read,
to discuss |
Op
tion al |
Homework questions? Day
31
Level C confidence interval estimate
of
population proportion p:
"One -proportion z-interval"
z* critical values: common ones are in table T
Day 31
Assumptions and conditions to use the CI
formula:
Sample "like SRS"--independence, no bias visible. n
< 10% of pop. P-hat normalish: np and nq > 10, using p-hat
for p. Day 31
Sample
size for desired ME and C Day
31
Why this ME "works".
Day
31
Lots of machinery and vocabulary:
NULL Hypothesis Ho : (Straw
man we collect evidence against. No change from Status
quo. )
Assume Ho is true. Look at evidence
(data). Is it inconsistent with Ho ? Then
Reject
Ho .
(How inconsistent with Ho is the data?
a little, somewhat, very? how do we measure it? Turn into
numbers---)
Ho : a specific model for the population, with
a specific parameter value.
Example (suppose I hadn't told you...): Green shoebox
is full of 0's and1's. I tell you Equal numbers.
Ho : p = .5 (proportion
of 1's is 50%) po for a general label.
Is your sample (n = 30) far enough
away from .5 to say that I'm lying? Suppose you believe I
undersupplied
1's:
HA : p < .5 (one-sided
alternative
hypothesis: What you
hope /fear /would
like to prove)
How do we measure "far enough away?"
IF Ho
is true: how far out (weird) is your p-hat?
IF p
= .5, how far from the "real" p is your
p-hat?
po = .5
Distribution of p-hats is approx. N(
),
N( .5, sqrt(.5 ·.5/30)), N( .5, .091) (Usual
assumptions.)
Suppose you got 12 1's. p-hat
= .4. IF p
= .5, p-hat = .4 has a z-score of -.1/.091 = - 1.095 ~ -1.10 Sketch
the Normal.
If you know your z-scores,
this is meaningful. A more universal measure is the
P-value: The
probability, assuming Ho
is true, of observing the result we have (or one more extreme)--if
we could do the experiment again... Strength of evidence against
Ho(thus
for HA)
In our example: The probability of getting a p-hat of
.4 or below, IF p = .5.
Sketch
on the curve.
The "tail" below z = -1.10. From normal table, .1357 ~
13.6%.
So
P-value = .136. Not so unusual;
happens more than 1 in ten times (13-14 in a hundred). Suggestive
but not "significant" by most people's standards.
Read the text. Read it again..... Do ActivStats...Read it
again...
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