Math 151 , Spring 2006, Day 36 Fri. April 28  Hit reload ...AFTER class

Exam 3, Next class 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 problems.  Check the link to see what's appropriate.
Day 36: (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?
+ + + +Postpone the rest + + + + + + +
A.  Use the T-table to decide these questions: 
a)  Ho: p = .3 vs.  HA: p>.3.   z from p-hat is 2.12.  Is it significant at the .01 level? .05? .10? 
b)  Ho: p = .3 vs.  HA: p not = .3.   z from p-hat is 2.12.  Is it significant at the .01 level? .05? .10? 
c)  Ho: p = .3 vs.  HA: p>.3.   z from p-hat is 3.16.  Is it significant at the .01 level? .05? .10? 
p. 387, #11 (use p.397--CI's & Tests)

Read,
  to 
discuss 		 Optional 
Exam 3 Monday, next class, 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.
Fay's review will be  6pm Sunday evening, Math Clinic.  "Look over the  sample test (and by look over I mean actually try to do it - identify  formulas, or possible formulas, needed for each question.  Identify  the key numbers - n, p, µ, p-hat, q...and all that jazz.  Anything  that will be helpful for an individual question.  Just familiarize  yourself with it.)  Bring in questions. )". 
SRS will be available after class today, briefly, then again after the groundbreaking ceremony and panel:  3ish? (Tell me you're coming to see me).  I'll be in the office after 9:15 Monday morning.
Sign-in sheet: indicate if you want to start early (after 9:30) or late Monday.  See me if you have other difficulties with the time.
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<>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

Continuing with Hypothesis testing (often called Significance testing)
Look at dotplots for our shoebox, and for (simulated) flips of a coin:  Ho: p= .5, Ha: p<.5. 

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

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

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<>Questions for exam?
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Start here Wed:
Table T (A-53)  bottom row is z-values.

What if you don't have the Z-table but only have the T-table (Table p. A-53)?
What if you have a demanded level of significance, alpha?
"Critical value" --the z* corresponding to your alpha (p.394-5 )
   T-Table: a limited list of probabilities  across the top row:
            = Right tail values for the bell curve distribution.  (and double that for equal-tails)
        The value in the bottom (infinity or z*) row under the probability is the corresponding standard normal value.
        "z* is the upper p critical value of the standard normal distribution."
  Do this: Find your z from the data. Make a sketch of the normal curve and mark z on it.  Mark the direction(s) of Ha.
    (If your z is in the direction of Ha , continue.  Otherwise the results are hopelessly not significant: you can quit.)
Find the two z*'s in Table T (p. A-53) that bracket your z (ignore minus sign).  Find the corresponding p's.
    e.g. z =1.83

Two tail p         .10     .05      .02
One tail p   ...   .05     .025     .01 ...
infinity(z*)      1.645 \/ 1.960    2.326
                    z = 1.83

Notice as the z's increase, the amounts in the tail(s) decrease.
Test is significant at the bigger bracketing probability; not sig. at the smaller. For z = 1.83,
One sided: P-value is less than .05 and greater than .025
       Significant at the .05 level,not at the .025 level
Two sided: P-value is less than .10 and greater than .05
       Significant at the .10 level,not at the .05 level
If you have a specific demanded significance level, compare it with these levels.
Give P-values if you can! (more information)

Confidence Intervals and Hypothesis Tests: (p. 397)
 Suppose you're interested in  Ho: p = .3 vs.  HA: p not = .3  ( two-sided alternative).  If your 95% CI for p DOES NOT include the po value (.3) , then you can Reject Ho at the .05 level (.05 = 1.00 -.95).  This is approximate, because we use different calculations for the standard deviations, but good enough if the CI is not close to the po.

More about decisions in testing.   See also inclass remarks, Day 35
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