MATH 251, P & S I, Fall 2011, Mon. Sept. 12,Day 8. After class, cleaned up, Homework especially..  Hit reload!

Day 8, Monday. 
Reading: Normal distribution, pp.54-64. 
Read ahead:  Normal quantile plots, 65-67; then Ch. 2

Hand in:  *?!?At least one more of the SPSS problems from Day 6
(All are due Friday)
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1.126 (forward), 1.128 (backward) (standard normal table)
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Always sketch the curve, mark the area(s) you need.
B. Simple warmup: Non-standard normal, table problems: 
    X is normal with mean 3 and s.d. 2. Find: 
    The proportion with X<1.5.  1.5 < X < 4.5. 

p. 63, 1.105 & 106 test scores, proportions

1.144 (osteoporosis)  Also sketch both curves on the same axis.
1.145 a, b (pregnancy)  (c will be assigned later) 
p.77 1.176d    (75's are Raw scores.  You could transform each to the N(100,20) distribution, if you remembered your formulas from parts a and b, or (shorter) you can find the percents asked for directly from the separate grades' distributions.  In each case you've found the percentile for  a grade of 75.)

C.  A small difference in means may give a surprisingly large proportional  difference in tails: 
a) Return to the data of 1.165, p. 75&6, and calculate what proportion of Females score below 450 and what proportion of Males score below 450.  Answer this:  The proportion of Males scoring below 450 is ____ times  the proportion of Females scoring below 450.
b)  Some of the difference in  (a) may be because the Male s.d. is larger, not just the difference in means.  Recalculate the proportion of Males who would score before 450 if their mean were still 565 but their s.d. 49 (= F s.d.)  The proportion is now ______.
This assumes, of course, that the Normal model holds up into the tails;  always questionable.

D. What proportion of pregnancies last 310 days or longer?  (see 1.145).
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"Backward."  Answer book gives z's to 4 decimal places.  Be content with the 2 places in Table A, unless otherwise instructed.)
E. X is normal with mean 3 and s.d. 2. Find:  The x for which 30% of the observations are smaller than it. The 30th percentile.
p. 64, 1.107, 108  ISTEP percentiles

1.145c  pregnancy, more
1.146  Normal quartiles, general, pregnancy  (The Table will only give you "between .67 & .68").  The answer book (or SPSS) gives .6745; use that for the next 2 exercises)
1.147 IQR for normal dist.
1.148 Outlier rule for normal
1.149 Normal deciles, potato chips

 Read, discuss 
 



Optional 

Normal density

1.127 (forward), 1.129 (backward) (standard normal table, more practice)
1.130 & 131  (Wechsler WAIS, more practice)

X is normal with mean 3 and s.d. 2. Find the x for which 80% of the observations are smaller than it.  The 80th percentile.

Normal curve template (Where you can count squares)

Normal practice handout Overview, worked problems, sample quiz/exam problems with templates you can count squares on.

 

Use   Normal Density Curve Applet  http://www.whfreeman.com/ips7e/  (or theapplet for ips6e, etc.) to check on all your Normal calculations!  (The Applet goes by .02's, and the text by .01's so the answers may differ slightly)

 
 

 
For D: [In 1973] the following item appeared in Dear Abby's "advice" 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?!?]

Quizzes returned. Problems worth 9, 16, 7 points, Total 32. Mostly very good; everyone 29 or higher..
--The smallest value IS the minimum even if it's an outlier; likewise for the largest.  The decision in a boxplot to where to end the whisker and start putting dots is not set in stone. Even if most computer programs use a similar rule, it may not always be a good one.  Here the so-called outliers don't really lie far out; they look more like just a thinning in the tails.. 
--Hospital nurses get paid more than office nurses, but not a lot more.  The median for office nurses is lower than that for hospital nurses, but higher than the first quartile for hospital nurses. And the maxes are about the same. The shapes are very similar, symmetric and probably normal-ish.   There's more spread in the office nurses' pay, so range and interquartile range are broader, and they are a bit less than the hospital nurses', with the hospital-office differences between the 5-number summary numbers increasing as you go lower.  (I was generous grading this--)
--Stemplots:  Do them like you're tallying, going thru data in sequence and writing the leaves on the stems.  Searching for smallest, then next smallest, etc. is extremely inefficient and error prone. (Rewrite with ordered leaves afterwards if needed)  May be possible for n = 15, but the more data, the  harder it gets (Lots harder: Like n2) .  Three people did them horizontally--that is an invention of this class; I've never seen that done.  But it's back of the envelope, quick and dirty, so no points off.
--Std. Dev. mostly good.  n-1 degrees of freedom:  Dimension of space of the n (x-xbar)'s (since they sum to 0)

HW questions? Day 7   How is SPSS going?  Day 6
     Morganstore link; For using Macintoshes.(Both on back pages)

Continuing Normal distribution--tables:  Details Day 5 , outline Day 7
   Normal Density  Applet  http://www.whfreeman.com/ips5e/
   Standard Normal N(0, 1).  Our tables give area to the left of a z value.  Table A, front flyleaf
   OPTIONAL aids:  Normal curve template (you can count squares), Normal practice handout

Normal all done today.
Quiz on Normal distribution (68-95-99.7 rule, standardizing and table use):  Friday or Monday, depending on how many questions we have Wednesday.

NEXT: How do you know if it's safe to treat a data set as if it comes from a Normal Density model?
Let SPSS draw a normal curve with the same mean and s.d. over its histogram; or use SPSS to make a Normal quantile plot p. 65-7 (handout next time):

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