|
Hand in: - - - - - - - Chapter 4, intro- - - - - - - - |
Read, to discuss | Optional (more
practice) p. 89, 3.53 ("backward x")
For next chapters: Do now if you need the practice: |
= = = = = = = = = = = = = = = = = = =
Applet: Normal Density
Curve http://bcs.whfreeman.com/bps4e
Handout:
Normal probability practice
Review:
starting with"raw" x's to area: Day8
Recap: "What proportion"problems: x's to proportions:
Draw picture, label with x's and z's mean, + s.d..
Mark desired area, roughly.
Standardize your x's. Use your z's to look in
the table for the area = proportion(s) to the left.
Subtract areas (never z's!!) if necessary, to find answer.
Homework questions? Handout: Solutions p. 87, 3.46 surprising difference
in tails
p. 80-81 3.11 and 3.12 (locomotive
adhesion, 2 dist's)
A. , What proportion of pregnancies last 310 days
or more? Find Mean and s.d. in p.74, 3.7
z = (310-266)/16
= 44/16= 2.75. Area above 2.75 = .0030. 3 in a thousand! Pretty
rare!
Why do I ask? (see "San Diego Reader" below )
Is "San Diego Reader" one of
the 3-in-a-thousand, or is she lying? (this is the kind of
question we deal with in Significance Testing, part 3 of the
course) Discussion
New: Going from area to x: Day 8
"Backward problems" "What raw (x) value has area ___ to the left/right of
it?" BPS4e pp. 81-83.
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. x
= mean + z ×(s.d.)
- - - - - Next: start Ch.
4.- - - - -
Relationships: (BPS4e Ch.4, at first
to p. 98)
Two Related quantitative variables (We used side by side
stemplots, boxplots, histograms to relate a quantitative variable to a
categorical variable)
"Just Related" or "explanatory &
response?"
(Scatterplots)
explanatory = independent
= "x"
= horizontal axis ( = "cause", sometimes
but not always)= predictOR
response = dependent
= "y" =
vertical axis = ("effect
") =predicteED
(Living histograms: Height vs. weight, Height vs. gpa)
Discussing Scatterplot
General
Pattern
Deviations
Clusters?
Outliers? (label if possible)
Form (linear, curved, ...?)
Strength of relationship (how unfuzzy)
"Weak, moderate, strong"
Direction
Positively associated: y increases as
x increases (generally).
Negatively associated: y decreases as
x increases.
**[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.Abby's answer was consoling and gracious but not very statistical:
San Diego Reader
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?]| Sievers home | Math151- Fall08/Dayf11.htm | 10pm | 9/22/08 |