| Hand in (All D&V)
Ch. 19p. 386 (including parts done ahead) 5, 6 Conclusions. Do these with the "Don't misstate..." section, pp. 361-2. 9 Cars A. Use the Normal table to find z* for a 99% CI (This is the z* for which 99% of the area is between -z* and +z*). Find z* for a 90% CI. (Text p.358 shows that z* = 1.645 to 3 decimal places. Normal table only gives 2 places.) Check your results by comparing with the corresponding results in Table T p. A-53. 11 Ghosts (Do rest.) 13 Teenage drivers (Do if you didn't) 21 Rickets 3, 4 Conditions 16 Local news ME, C, n pp. 356-7, 361-3. Problems p. 368
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Read,
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Optional |
Homework questions?
Definition
and computation of CI: introduce
table T, and Assumptions/conditions. Chapter 19
Day
29
Sample size for desired ME and C; Why this
ME "works". Day 30
Level C confidence interval estimate
of
population proportion p:
"One -proportion z-interval"
Start here Wednesday:
Why this ME "works".
Day 30
Lots of machinery:
NULL Hypothesis Ho : (Straw
man we collect evidence against)
Assume Ho is true. Look at evidence
(data). Is it inconsistent with Ho ? Reject
Ho .
(How inconsistent? 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%)
Is your sample (n = 30) far enough
away from .5 to say that I'm lying? Suppose you believe I cheated
on the 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?
Distribution of p-hats is approx. N(p, 
),
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...
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.
Alternative hypothesis: Null
hypothesis is often a particular parameter value. Alternative is
something "different."
p < .5 You have
reason to believe I skimped on the 1's.
One-sided
OR p > .5 You have reason to believe I put
in more 1's than 0's. One-sided
OR p not = .5 You believe the 0's and 1's are not
equal, but don't know which way. Two-sided.
P-value concept needs refining: For One-sided alternatives, P-value
is the single "tail" beyond our observed statistic, in the direction
of the alternative hypothesis.
For a Two-sided alternative, P-value is "double the tail"
beyond our observed statistic, because we could be "as or more extreme"
in either direction!
Example: If your alternative is HA
: p not = .5, there is probability .136 below z = - 1.10,
and probability .136 above z = + 1.10, so the P-value = 2· .136
= .272. 1 in 4? Not unusual at all.
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