Math 151 , Spring 2006, Day 34 Mon. April 24  Hit reload ...After class

Exam 3, Friday (Day 36, April 28)  Covers work Chapter 13  thru today's HW.
  Covers Part III, experiments (one-factor), diagrams, several designs.  (Day 23HW on).  Part IV (what we did), and V thru Monday Day 34    Sample exam problems.  Check the link to see what's appropriate.
Day 34: (Re)Reading: Chapter 20+21 thru p. 392 (Activstats is good here too.) 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) 
No new HW assigned:  Repair Day 33 HW and hand it in Wednesday, come with exam questions and remaining HW questions.

Postpone all:
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. Handout of Sample problems. (See link, top of page) 
We have 15/20 = 75% 16/22 = 73% of our intervals containing p=.4.  Closer to the designed 68% Confidence level.
Link: Exploratory vs. Confirmatory
 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--and you have to know when to use which formula!
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!
<>Homework questions: Day 33
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.
Check the sample problems Handout to see what's not appropriate now.
Class spent working HW, mechanics and meaning of P-value.  Pick up here next.

Continuing with Hypothesis testing (often called Significance testing)
Use CI to estimate true value.  Two-sided tests.    Notes:  Day 33

How "strong" is our evidence?  Informally/descriptively--
        Take P< .05 to be "moderately strong"--1 in 20 chance of seeing something this weird (again) if Ho is really true.
"Statistically significant" result (p.256):  An observed difference is too large for us to believe that it is likely to have occurred naturally (i.e. because of random variation.)  add: If Ho  (no population difference) is truly the case.

Especially if we must make a decision to Reject Ho  (or retain it)---
  Set "benchmark" or "cutoff" level  "alpha"  "significance level":  (p. 393-4)
        If  P-value is less than alpha, we say the test is "significant at level alpha"
                      (Seeing the result (again) would be rarer than alpha, if the null hypothesis is true)

Different fields/ questions use different alphas.  If rejecting  Ho is startling, or costly, want a smaller alpha.
  Usually round numbers:  .10 (1 in 10), .05 (1 in 20), .01 (1 in 100), .001 (1 in a thousand) etc.
    Smoke detector : P = 0.4% = .004.  IS Significant at .10, .05, .01 levels.  NOT significant at .001 level.

Cautions:  (p. 394)
   P = .0499 "Is significant" but P = .0501 "is NOT significant" at .05 level.  Best to report P-values, whether or not you use an alpha to base a decision on.
  "Statistically significant" difference isn't necessarily either  *large*  or *of any importance*.  (With enough data, you can detect even  small deviations from the null hypothesis.)

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