| Hand in (All
D&VCh6 unless otherwise noted) 68-95-99.7 rule: Ch6 p. 99ff: Sketch normals&mark, do questions. 11 guzzlers 14 Rivets (d is a judgment call--depends on circumstance to some extent...) 13 downhill (for d: Data is in order already. Stemplot or histo-by-hand (widths=1) is quicker than going to SPSS.) 18 %white (for d, your answer can be rough. Noting where Q1 is may help in guesstimating.) p. 99, #9 Professors + + + + + + + + + + + + standardizing: Ch6 p. 99: Sketch each Normal model and label its axis with both the "real/raw" values and the "z" values. Mark the observations on the pictures, do questions. 5 temperatures 6 placement exams = = = = = = = = = = = = = Table use: Always sketch the model first, mark the area you are looking for! Find the answers using Table Z, Appendix p. A-30. Check your answers with one of the Technology Normal tools (see above) p.101 #20, 22 (Note: 22d finds what numbers from the 5-number summary?) &&&&&&&&&&&&&& Do what you can of the following, KEEP for next assignment Raw data problems. Do unstarred parts with table Z. "Backward" parts are marked with *--do them with a technology tool (see above) p.102, 25 Cholesterol a, b, c, d*, e* 26 Tires a, b, c, d*, e* 28 Body Temperatures: a, b, c* Also: I have a theory as to where the "wrong" number 98.6F came from. Early work on temperatures all took place in Europe. Convert 98.6F and 98.2F to Celsius (subtract 32, and divide by 1.8). What's my theory? |
Read,
to discuss |
Optional
Use technology to check on & picture your Normal models: Moore website http://www.whfreeman.com/scc/ Statistical Applets, Normal Curve. Uncheck the 2-tail box for most uses. OR ActivStats Normal Density Tool for you : for best setup* Use AS30-2 "Normal distribution based Confidence Intervals tool" CAUTION: Don't hit the Enter key! It closes the tool-box! Normal Prob. Plots (D&Vp. 94-95). - - - - - - - - |
What
percent are further than 3 s.d. from the mean? What
percent
are higher than 2 s.d. from the mean? Etc. Standardizing: A way of comparing an individual
against
its pack.
Comparing individuals from different packs, each relative to its own.
Removes "units of measurement" from the discussion.
Enables use of the standard normal table.
Examples: Wechsler Adult Intelligence Scale scores used to be
approximately
N(110,
25)
A score of 85
is 1 s.d. below the mean. Computation: z = (85
–
110)/25
= (–25 raw points)/25
= –1 s.d. from mean.
(About
the 16th percentile--16% get scores < 85)
145
is
how many s.d.'s above the mean?
Computation: z = (145
– 110)/
25=
(35 raw points above mean)/25
=
1
2/5 = 1.4 s.d. above mean
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ First
standard normal table
use,
then with "real" values~ ~ ~ ~ ~ ~ ~ ~ ~ ~
Standard Normal N(0, 1). Our tables give area to the left
of a z value. TableZ, Appendix E, A-50
Using standard normal table: See D&V p. 88. (Wrong
side of graph is shaded in my text)
z |
.00 .01 .02
.....
...|
1.4 | .9192
.9207 .9222 ....
P(z < 1.40) = .9192, P(z < 1.41)
= .9207 P(z < 1.42) = .9222.
?z has more than 2 dec. places? Round to 2.
Sketch the density, mark the area
you're
looking for.
Figure out how to get it using areas to
the left of one or more z-values.
Think cutting up paper
bell-curves.
(Remember whole area is 1.) Like handout.
Example: Proportion of observations between 0.5 and
1.4
P(0.5 < z <1.4) =
Proportion of observations below 1.4 minus
Proportion
of observations below 0.5
P (z < 1.4) - P(z < 0.5) = .9192 - .6915 =
.2277
.
Example: Proportion of observations above
0.5,
P( z > 0.5) =
ONE minus proportion of observations below 0.5,
1 - P( z < 0.5) = 1-.6915 = .3085
.
Reading
table "backward":
What z value has area ..... to the left/right
of it?
Sketch roughly.
Restate
(if
needed) as "What z value has area A to the LEFT of it."
Look
in body of table for the value closest to A.
Go
to edge(s) of table to find what z that goes with.
Example: "What z value has 10%
of the observations above it?" This is the same z as the one for:
"What
z value has 90% of the observations below (to the left of) it."
(What z is the 90th percentile.)
Find
in the table .8997 and .9015 -- .9000, our number, is
between
them.
.8997 is a little closer to.9000, so use it.
For .8997, the z value is 1.28. 1.28 is the
90th
percentile.
1.28 has 10% of the observations above it.
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
- - - - - - - - - - - - - - - - - - - - -
"What proportion"problems:
(D&V p.90-2: "....I", "More..." question 1) http://www.whfreeman.com/scc/
* AS6 Normal Density tool: Use AS30-2 "Normal distribution
based
Confidence Intervals" tool for best setup.CAUTION:
Don't hit the Enter key! It closes the tool-box! To
use it from Tool1 from the menu bar in Ch. 6: Right click for
menu.
Choose Show Buttons. Choose Show Flag Values, Mean,
StandardDeviation;
Real Values. Now you can type in mean and s.d. and the mean
+ 1,2,3 s.d.'s will show on the axis. CAUTION:
Don't hit the Enter key! It closes the tool-box! To
register
a typed number, click in a different box.
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