Relation of m (margin of error, half width),
C (confidence level), and n (sample size), (and sigma)
C and z* get bigger and smaller together
(bigger C means bigger z*, and vice versa) (standard normal sketch)
m = z* (sigma)/ sqrt(n)
Want bigger C? Must accept bigger
m. Trade off confidence vs. accuracy.
But bigger n will make smaller m.
This makes sense: bigger sample size, more info-->more accurate estimate.
(square root makes it Expensive: have to quadruple n to make m half as
big)
So smaller m can be achieved only by
accepting lower confidence
level (smaller C),
or by increasing sample
size (bigger n).
Sigma: We can't change it, it comes with the population. But bigger sigma (more population variability) will give bigger m (wider CI), i.e. less accuracy in prediction (for the same C and n).
Planning ahead: Choose sample size big enough to satisfy
desired: margin of error, confidence level.
Given C and m (and sigma), find n.
Method: Use C to find
z*. Plug in to formula for m, and solve for n. Or memorize
formula for n and plug in to it.
n = (z* sigma / m)2 Note:
z* sigma still on top. m and n change places, and whole thing is
squared!
Round up! If you get n = 5.06, you need a sample of size 6 to get
your margin of error as short as you want.
~~~~~~~~~~~~~~~~
Sec 6.2: "Significance tests use an elaborate vocabulary,
but the basic idea is simple: an outcome that would "rarely" happen
if a claim were true--is good evidence that the claim is NOT true."
(p.314)
| Sec.6.1 (problems marked FRI were given
on day 28 also) .
FRI 6.3 density of x-bar, and confidence intervals This problem combines the pictures 6.2 and 6.4 For part d, to draw the confidence interval: just choose any point on the horizontal axis of your graph to be x-bar. Measure off the distance m (half the width of the shaded interval) and extend a bar m wide to the left and the right of your point,below the curve. (Like fig. 6.4, the bars with arrows at the ends. The red dots show what the x-bar is for that confidence interval) Choose another point, and repeat.. If your first x-bar was in the shaded interval, pick your second outside the shaded interval, and vice versa. You should note that if x-bar is in the shaded interval, then the confidence interval bar covers mu (280) and if x-bar isn't, then the bar doesn't. = = = = = = = = = = = = FRI 6.5 IQ test scores Read pp. 312-13 before doing this one. = = = = = = = = = = = = Cautions; general review and extension FRI p. 314 6.14 internet, response rate FRI p.317, 6.19 newts FRI p. 318, 6.22 men/women CI's = = = = = = = = = = = = Hand in Monday: Sample size for C.I., review p. 3.11, 6.10, 6.11, 6.12 p. 315, 6.16 enlighten the unstatistical 6.17hotel mgrs. Read Sec. 6.2. Write down on a separate sheet 3 new terms that you will need to understand. |
Read, to discuss
6.13, 6.15 (cautions)
|
Optional |
| Sievers home | Math151-Sp01/Day29.htm | 11pm | 4/12/01 |