Math 151 , Spring 2006, Day 35 Wed. April 26  Hit reload ...After class

Exam 3, Friday (Day 36, April 28)  Monday, Day 37, May 1.Covers work Chapter 13 (part)  thru Friday's HW.
  Covers Part III, experiments (one-factor), diagrams, several designs.  (Day 23HW on).  Part IV (what we did), and V thru Friday Day 33 HW    Sample exam problemsCheck the link to see what's appropriate.
Day 35: (Re)Reading: Chapter 20+21 thru p. 392 (Activstats is good here too.) (exam to here.) Then continue (Alpha levels) through 395.  Lightly through Error types and Power . Read What can go wrong p. 401 and the rest. (SPSS won't do proportion computations, but some other programs do; it's good to have an idea what you might see, p. 402.)
Hand in (All D&V) Wednesday!

Two-sided:  For some reason, D&V don't model or assign any 2-sided problems (except #8).  We need to be used to them for later, so here are a few.
A: b) Use your green shoebox result to do a Two sided test against the null hypothesis p = .5.
Ch. 20, p.387 #7, Find the mistakes The first mistake is that both hypotheses are written with incorrect notation.  The second is that the alternative hypothesis is chosen wrongly.  I would write the company's goal as "more than 90% succeed"--I think that makes it clearer what structure to use.
Ch. 20, p.387  #8 Find the mistakes
From ActivStats, copied here:
 MRA-304-2:  Kerrich Coin Toss  While he was a prisoner of the Germans during World War II, the British statistician John Kerrich tossed a coin 10,000 times.  He got 5067 heads.  Take Kerrich's tosses to be an SRS from the population of all possible tosses of his coin.  If the coin is perfectly balanced, p = 0.5.  Is there reason to think that Kerrich's coin was not balanced? 

 TRE-396-9:  Store Checkout-Scanner Accuracy (adapted from Activstats HW):
In a study of store checkout-scanners, 1234 items were checked and 20 of them were found to be overcharges (based on data from "UPC Scanner Pricing Systems: Are They Accurate?" by Goodstein, Journal of Marketing, Vol. 58).  Before scanners were used, the overcharge rate was estimated to be about 1% . Based on these results, do scanners appear to give a different rate of overcharges than the old method of keying in the price?  (All items had to have individual price tags; scanning is much less labor-intensive.)  Do the steps, finding the P-value and stating a conclusion. 
= = = = = = = = = = 
"Significance" Ch. 21, p. 404 
1 P-value
3, 4 Alpha 
5, 6 Significant?

Read,
  to 
discuss 
Optional 
Exam 3 on Friday, next class. Monday, day 37, by popular demand. Handout of Sample problems (last time). (See link to updated version, top of page) 
 I will give you, on the test, the formulas for SD(p-hat), SD(x-bar), n for given C and ME.  The rest you need to memorize.
I will give you the Z and the T table; but be ready to find the z* for a C not in the T table!
Hypothesis test questions on the exam: I will only ask one-sided hypothesis test questions.  "Moderately strong" evidence will be taken to mean a P-value of .05 or less.
FROM FAY: Office hour today 12.30-1.30 and a review  session on Thursday night 7-8.  Sunday: watch your email.
Sign-in sheet: indicate if you want to start early (after 9:30) or late Friday.  See me if you have other difficulties with the time.
- - - - - - - - - - - - - - - - -
<>On the yellow pad circulating, for your shoebox sample,  give your test results:
  # of 1's / p-hat / z-statistic /  P-value /  P < .05? Y/N

Homework questions:
Day 33
In class:  If your P-value is not "significantly small" (.10, .05, or less) but is in the direction of your alternative hypothesis  (P = .25 or so), there are two possibilities:
1) The real p is actually the null hypothesis p (there IS NO difference between your population and the null hypothesis population)
2) The real p is different from the null hypothesis p (there IS a difference between your population and the null hypothesis population) BUT  it's not a big enough difference to detect with the sample size you used.  (The difference is too small and/or the sample size is too small).
(Or--once in a while--we just got an unusual sample that looks like the null hypothesis population although it's from a quite different alternative.)
The machinery we've developed gives us no way to distinguish between these possibilities.  So it's not safe to say that your population is the same as the null hypothesis just because your P value is not significantly small.

Questions for exam? 
Start here Friday:
Continuing with Hypothesis testing (often called Significance testing)

Use CI to estimate true value.  Two-sided tests.    Notes:  Day 32

"Statistically significant" result, and  "alpha"  "significance level."    Cautions.  Notes Day 34


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