Math 151, Day 9, Wednesday, Feb. 16, 2001 Final
version
Hour exam, a week from Friday (Day 13). Covers
thru Monday's assignment.
Homework notes: Just because SPSS will do some of your
work, don't abdicate responsibility. You still have to label your
graphs, tell what you're counting or measuring. Make conclusions if any.
And if you have a bunch of output and the desired answers are in there
someplace, you have to find them and mark them for your reader/self.
Since they are printed on paper, and you all own pens or pencils, this
is not too onerous.
Standardizing, Day 8
Normal area problems, Day 8
Got to here, day 9, will
start here on Day 10.
"Backward problems" "What
raw (x) value has area ___ to the left/right
of it?"
Sketch the curve, labeled with x values and z values, and the
Area, 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.
Convert
the z to an x: z is the number
of standard deviations above the mean.
Multiply z by the size of 1 standard
deviation. Now you have distance above
the mean, measured in raw units.
Add the mean.
Now you have the "raw" value x.
Example: What x
value
has 10% of the observations above it? This is the same
x as the one for:
What
x value has 90% of the observations below
(to the left of) it.
The table gives z = 1.28, approximately. The Wechsler score x=
mean
+ z (s.d.) = 110
+ 1.28 (25) = 142
Percentiles: a Wechsler score of 142
has 90% of the scores at or below it. 142 is the 90th percentile.
HW Day 9, Wednesday, Sept 19. (Re)read the section, (Re?)read
pp. 61-64, using the table "backward" for next time, and look at above
example. Summary, pp. 66-69.
Read ahead Ch. 2 (Examining relationships), pp. 78-91. Then we'll
continue with 2.2 (correlation)
Hand in
standardizing:
p. 56 1.56 SAT/ACT p. 65
1.64 (cf. batting avgs)
table use: Always sketch the distribution
first, mark the area you are looking for!
p. 64 1.68 a and b.Pregnancies
Also, What proportion of pregnancies last 310 days or more?
(see below.)
p. 61 1.58 (locomotive adhesion, 2 dist's)
p. 66 1.69 (Stanford-Binet,
"superior")
- - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Following is part of Day 10 asst.
"Backward Normal"Always sketch a normal curve
first,
roughly mark the proportion=area you are given.
p. 76 1.89 (soldiers' heads)
p.64 1.68 c (pregnancy)
p. 66 1.70 (z-scores of quartiles) |
Read, to discuss
|
Optional (more practice)
1.67
+Learn to use SPSS to find
the proportions--
manual pp. 58-59:"CDF"
- - - - - - - - - - - - -
Part of Day 10:
"Backward"
p. 62 1.60 (WAIS)
+Learn to use SPSS to find
the values-- manual pp.58-59:"IDF"
|
[In 1973] the following item appeared
in Dear Abby's column:
Dear Abby: You wrote
in your column that a woman is pregnant for 266 days. Who said so? I carried
my baby for ten months and five days, and there is no doubt about
it because I know the exact date my baby was conceived. My husband is in
the Navy and it couldn't have possibly been conceived any other time
because I saw him only once for an hour, and I didn't see him again
until the day before the baby was born. I don't drink or run around, and
there is no way this baby isn't his, so please print a retraction about
that 266-day carrying time because otherwise I am in a lot of trouble.
San Diego Reader
Abby's answer was consoling and gracious but not very statistical:
Dear Reader: The average gestation
period is 266 days. Some babies come early. Others come late. Yours was
late.
The question here is not whether the baby was late. That
fact is already known. At issue is the credibility of the length of the
delay. Ten months and five days is approximately 310 days, which means
that the pregnancy exceeded the norm by 44 days. [How unusual is that?]
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