Math 151 , Day 34, Monday, April 23, 2001

>EXAM 3 Friday, in class, closed book.
Ch. 6, through 6.3 ; Also Ch. 4, everything but probabilities in a finite space.
>Quiz:  If you got a B+ or lower, you may try a third time (max grade A--), today before or after class, or at 12:30 at my office.

Significance test (P-value) vs. Hypothesis test (fixed alpha:  Accept H0)

Questions on Homework, Ch. 6.   Ch. 4?

Practice for the exam:  Handout: An old exam to work through.  Solutions outside my door + on reserve (soon)
p. 255: 4.63, 64 (harder), 65.   p. 360, 6.75, 76.  Old hw assignments--don't slight the "word" problems!
(Remember solutions manual is on reserve, + in Math Library)
Definitions and things in boxes; end of sections summaries.  Chapter summaries pp.251-252, pp.358-60

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Chapter 7, Inference for Distributions (we'll do 7.1, 7.2, and the first segment, to p. 414, of 7.3)

Inference for means, using xbar from a SRS:
Large n
 Sigma known          Sigma unknown
Small n
 Sigma known          Sigma unknown
normal
Population is 
not normal
  Xbar is normal,
find z using sigma		  Xbar is normal,
find z using s.		 Xbar is normal, 
find z using sigma		 Xbar is normal, 
Find t using s
Xbar is normal-ish (CLTh), 
find z using sigma		 Xbar is normal-ish (CLTh), 
find z using s		 Unrealistic (See p. 381)
If you can't use t,
Find a statistician

t-distribution family:  like standard normal only slightly fatter in the tails.  Mean = 0. Symmetrical around 0.
    "Degrees of freedom" tell which member of the t family.  t(k) is the t distribution with k degrees of freedom.
    Lower d.f.--fatter tails.  Higher d.f.--more like standard normal.
    Table C:  upper tail:  probability <--> "critical" t-value.

Start working on green box:
Assume Normal population .  Mean mu, s.d. sigma, both unknown.
Take SRS, size n, find xbar, find s (sample standard dev.)

"Standard error of the (sample) mean" = s/sqrt(n)    Standard deviation of xbar, estimated from the data.

Standardizing xbar with s instead of sigma results in
t =    xbar - mu
         s/sqrt(n)            the one-sample t statistic
which has the t-distribution with n-1 degrees of freedom.

We'll now repeat all the stuff from Chapter 6, only wherever there was a z, we'll substitute a t.

HW Day 34 final
Review.  Read about Gosset, p. 364, and Sec 7.1, at least thru p. 369.  We'll start by doing some by hand, then turn the computation over to SPSS.
Bring questions on Ch. 6 and Ch. 4. 
Hand in: 
Sec. 7.1   "Standard error" & t-distribution family
p. 364 7.1, 7.2, 7.3		 Read, to discuss Optional 
Review: 

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