| Hand in
Monday:
A. New Shoeboxes: On a Separate sheet: (2 shoeboxes. )The shoeboxes are outside my door if you missed doing them in class. For each sample of size 4 from a shoebox, write down the values, find the mean, (know which box you got them from: White #s, green box. Yellow, red top.) and tell whether you believe the population mean for that box is 20, or something bigger. (Your gut feeling.) Does it help to know that the standard deviations for the shoeboxes are both 4? ( Bring your sample numbers and xbars to class to pool.) (This is related to Chapter 15, where we'll learn the formal methods.) <>- - - - - - - - - - - - - - - - - - - - - - - - -p.352, 14.4 Using Table A to find z* The trick is to change from "C in the center between -z* and +z*" to "What? to the left of z*", to use Table A. You can check using the C to z* section of the Confidence Interval Excel sheet. - - - - - - - - - - - - - - - - - - - - - - - Sample size for C.I. (& review of CI computations)You can check using the bottom section of the Confidence Interval Excel sheet. p. 356, 14.10 Estimating mean IQ p. 358 14.24 Hotel managers p. 360, 14.33 calibrating a scale "Why C.I. formula works" p. 348, 14.1 density of x-bar, and confidence intervals. This problem has you illustrate the middle paragraph of Example 14.2, pp. 345-6. For part c, to draw the confidence interval: just choose any point on the horizontal axis of your graph to be x-bar (Like me at the board, my head being xbar). Measure off the distance m (half the width of the shaded interval) and extend a bar m wide to the left and the right of your point,below the curve (My arm length was m). (Like fig. 14.3, one of the bars with arrows at the ends. The red dots show what the x-bar is for that confidence interval) Choose another point, and repeat.. If your first x-bar was in the shaded interval, pick your second outside the shaded interval, and vice versa. You should note that if x-bar is in the shaded interval, then the confidence interval bar covers mu (280) and if x-bar isn't, then the bar doesn't. A few review problems: In practice, Ch. 16 Looking ahead in Ch. 15 Try this
one, on a separate sheet; will be assigned Monday. & & & & & Leftover
problems from
Day 30 &
& & & & & & & |
Read, to discuss p. 391, 16.3 environment p. 407, 16.31 sampling at the mall |
Optional (more practice) p. 389, 16.1 TV poll p. 391, 16.2 red lights |
New Shoeboxes: Take 4 from each, write them down (White from green box, yellow from red-top box) For HW, find means (for each box separately.) Know which box! Does that box have pop. mean 20, or some number >20? Your gut feeling. (Does it help to know s.d. for each box is 4?
Exam 4, Friday Nov. 17, Day 36. A week
from today. 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
today. You can do all but possibly 3d after
tonight's HW (3d is like 15.1); solutions available Monday.
# # # # # # # # # # # # # # # # # # # # # # #
# # # # # # # # # # # # # # # # # # # # # #
Confidence
interval estimate of a(n unknown) population parameter:
(Table
A, or Table C, t dist. bottom row)
,
n = (z* sigma / m)2
Still need to do this:
Look back at 11.36 and 38, p. 290. 38: "backward
normal" problem. From a proportion/probability, find a z*,
from that a raw value (here an x-bar.
Why does the formula work?
In practice: pp.
388-391
SRS--other random samples get other formulas.
Nonrandom
or biased samples simply can't do C.I.
Sometimes we can plausibly think of
data
as SRS from large population (rolling dice, repeated weighings on
scale)
--
For experiments, randomizing into groups allows us to use the methods;
but be careful about generalizing far beyond our "volunteers" type.
Ask how reasonably "like" a SRS the sample is.
Xbars are normal! OK IF 1) population is normal,
or 2) n
big enough for Central Limit theorem.
Outliers? Trouble (xbar is
sensitive).
Slight outliers ok (see next)
Skewness? "Moderate" sample size allows CLTh
to
overcome
all but strong skewness. (Numbers in Ch. 18)
Sigma for population is known. Rarely true in
practice.
Large n? Could
substitute s calculated from sample as "good" estimate of
sigma.
Small
n--Ch. 18, a slight modification of these methods takes care of unknown
sigma.
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
Start significance tests Monday
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)
Suppose someone claims that the average height of Wells women over the
years is 70" (5'10"). I take samples (151 classes) every
year. This year my sample has mean 62.81" (n = 20ish). Standard
deviation for heights of women in population is supposed to be about
2.5" IF the real mean is 70", my sample is extremely
improbable. Conclude the claim is Not true.
Need machinery to analyze less "obvious" results, build in effect of
standard deviation (if s.d. were 10" would my sample still be
inconsistent with the claim?) and sample size (if n were only 4 would
that change my result?) . Do 15.2 p. 363 if time.
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