| Hand in MONday . If you didn't do A. from day 34 (calculating P-value for the shoeboxes) do it now. + + + + + + + + + + + + + + + + + + + + + These are pretty simple, step by step. Read the book and do them. p. 366, 15.2 Older students Didn't do in class, but outline of work is at Day34 Stating null and alternative hypotheses p. 366, 15.3 Anemia (15.1, 3 done in class, + more) p. 366, 15.4 Student attitudes p. 367, 15.6 travel time p. 367, 15.7 stating hypotheses - - - - - - - - - - - - Test statistic: xbar to z p. 368, 15.8, 15.9, 15.10 (same old examples) - - - - - - - - - - - - Calculating p-value (one-sided) p. 371, 15.12, 15.13, 15.14 (Same examples). Calculate by hand. p. 371, 15.11, Applet. Do the one given (two-sided), then check your answers for 15.12, 13, 14 (one-sided) using the Applet: P-value of a test of significance . (Uses "raw" scale of xbars, rather than z-scores). & Postpone some more!& & & & Leftover problems from Day 30 & & & & & & & & These ideas are related to those in Ch. 15. p. 290, 11.39 Pollutants in auto exhausts For 11.39: You might want to know L so that if you tested your 25 cars and found a high value of x-bar, you would be able to compare it with L; if it was greater than L, you would go back to the manufacturer and say "I believe you sold me a batch of bad cars, because the chances of getting an average emission level this high if the exhaust system is working properly is only 1 in 100. It is more reasonable to believe the exhaust system is not working, than that we "are" that 1 in 100 possibility." p. 290, 11.38 Glucose testing If we use this cutoff level L to say that people (with a mean of 4 tests) over L "have diabetes", then the chances of declaring that someone "has diabetes" when they really are OK (with mean 125mg/dl) is .05. .05 or 5% is the chance of a "false positive" using this protocol, when the real mean is 125. & & & & & & & & & & & & & & & & & & |
Read, to discuss |
Optional (more practice) + + + + + + |
Your shoebox
results: Write your xbars , z's, P-values, and <.10 (Y/N) (one on each pad--yellow or
white). And, if you didn't last time, make a dot for each on
the circulating dotplot.
Exam 4, Friday Nov. 17, Day 36. This
Friday. As usual: One
sheet of notes; I will give you
tables. Covers Ch. 10 p. 257 on (Continuous models and R.V.'s),
Ch. 11 up to p. 286 only, Ch. 14, Ch. 16 to p. 391, Ch. 15 to p.
364. Sample
exam handed out Friday;
solutions outside my door/on reserve.
New
this afternoon: Excel
spreadsheet with graph of distribution of xbars overlaid on
distribution of population.
Jenn O'Neill remaining
TA hours
this week: Wednesday 6:30-8pm and in addition this week,
Thursday 6:15-8pm for anyone who wants to review for the exam
on Friday.
HW questions? Day
34
Exam questions??
"Statistics means
never having to say you're
certain."
Confidence interval Estimation made our best guess at an
unknown population mean.
Testing will investigate a claim made that the
unknown
mean is actually a particular value.
~~~~~~~~~~~~~~~~
Ch. 15: "Significance tests use
an elaborate
vocabulary, but the basic idea is simple: an outcome that would
"rarely" happen if a claim were true--is good evidence that the claim
is
NOT true." (p.363 top)
Day 34 for details. Summary:
Went through the game for one each of
Ha: µ > some value.
Ha:
µ
< some value. Did not talk about a two-sided hypothesis.
Didn't try out the applet.
Take data. Calculate test statistic. For
µ, test statistic is the z-score of xbar.
Is it an unlikely
result if H0 is true? Then that is
evidence
against
H0.
Measuring the strength of the evidence against H0 (a
common measuring stick for all distributions and parameters):
P-value of
a test: The probability, computed assuming
that H0 is true, that the observed outcome would
take a value as extreme or more extreme than that actually observed
(if
we could repeat taking-data again). p. 368.
The smaller the P-value, the stronger the data's
evidence against H0 ( for Ha).
For a test of µ , using xbar (sigma
known),
the P-value is
--the area of the tail beyond the observed xbar, in the
direction of Ha (one-sided)
(--or twice that area (two-sided).)
<>Applet: P-value
of a
test of significance automates this. (Uses "raw" scale of
xbars, rather than z-scores).
A "Significance level" alpha is a probability level
we
decide on in advance as being the "rarely" amount that
will
push us over into believing (well, sort of) that the H0
claim is not true. (Historically older
language
than P-value)
We tend to use simple benchmark numbers for it, like .10 (1 in 10),
.05 (1 in 20), .01 (1 in 100).
When the P-value is less than (or equal to) a particular
significance
level alpha (say .05), we say,
"The results are significant at the alpha = .05
level," or "The results are significant (P< .05)"
Next: more practice with these ideas, using table C for
significance levels.
- - - - - - -
Today, finally?NOPE: Look back at
11.36 and 38, p. 297. 38: "backward
normal" problem. From a proportion/probability, find a z*,
from that a raw value (here an x-bar).
Note that table C gives us another way to get z*'s for some
probabilities! Bottom row, "one sided P". The table is set
up to go from "tail" probability to z*, without having to calculate
"probability to the left."
| Sievers home | Math151-Fall06/Daym35.htm | 3:30pm | 11/15/06 |