| Moore sec.
4.3 Hand
in Wednesday
DIST. OF XBAR(S) These problems use only the mean and standard deviation. p. 243, 4.41 (lab measurements) p. 250, 4.50 These problems use either the Central Limit theorem, or the "sample mean of n independent observations from a normal distribution has a normal distribution." theorem (both on p. 244) p. 249, 4.51 cola (you did a, now do b) p. 247, 4.44 carpet flaws. Also draw some square yards and mark some flaws. p. 250, 4.53 auto accidents More problems: p. 243 4.42 unbiasedness, sample size p. 249 4.52 hypokalemia p. 249 4.48 dust Note, the dust actually weighs 123mg, but the weighings may not be accurate enough for us to find the actual weight. "Distribution of this mean" = "Distribution of means from all possible sets of 3 weighings from these scales." When I took physics, we did not have digital scales; they were balance beams; and we weighed everything 3 times and found the average. (Have you ever gotten on the scale, said "that can't be right!" gotten off and on again a couple times?) . p.250 4.54 (labeled 4.53?) pollutants; backward from value to probability. You might want to know L so that if you tested your 125 cars and found a high value of x-bar, you would be able to compare it with L; if it was greater than L, you would go back to the manufacturer and say "I believe you sold me a batch of bad cars, because the chances of getting an average emission level this high if the exhaust system is working properly is only 1 in 100. It is more reasonable to believe the exhaust system is not working, than that we hit that 1 in 100 possibility." A. Get 4 slips from the Birkenstock box (outside my door if you missed class). Record them, return them. Find their mean xbar. Find xbar - .841, xbar +.841, your "interval estimate" for the unknown mean of the box. Bring next time to compare. |
Read,
to discuss |
Optional
Extra credit, see LLN-game Extension to Wednesday |
Review Law of Large Numbers (day
27),
HW questions on LLN?
Mostly we have a fixed sample size n. How close
will Xbar be to µX?
Review Central Limit Theorem et al (day
27) :
Look at and add to Sampling Distribution of (sample) means
from 10 test scores.
"Fuzzy Central Limit Theorem:"
Data whose variation is due to many small
independent random influences will have an approximately
normal distribution.
Balls and pins, heights of women, etc.
- - - - - - - - - - - - - - - - - - - - - - - - - - - -
Chapter 6, preview:
SAMPLE from an UNKNOWN population.
Each person take 4 slips from the Birkenstock box,
find the mean, and your mean
+
.841.
Record these for yourself . This
is your "Interval Estimate" of the mean of the
Birkenstock
population.
Your "estimate"
of the (unknown) population mean µ of the numbers in the
shoebox
is your sample mean plus or minus the "fudge factor/margin of error"
.841.
Record
them also on the sheet going around, and draw
the interval on the graph transparency
going around.
If xbar =
8.0
7.159|_____________8.0_____________|8.841
| Sievers home | Math151-Sp04/Days28.htm | 8pm | 3/11/04 |