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Chapter 18, Sampling distributions: proportions 1, 3 Coin tosses 5 More coin 9 Loans 13 Apples 14 Genetic defect Sampling distributions: means 17, 18 Sampling distribution 19 GPAs 20 home values Sampling dist. of means, cont. p. 350 B): "Normal" body temperature 98.6 deg. on average. (Assume this is true.) Assume normal distribution, & s.d.among many people is 0.6. What is the-- Probability that one (random) healthy individual's normal temperature is above 98.8? Probability that the mean of a sample of 4 is above 98.8? Probability that the mean of a sample of 36 is above 98.8? Probability that the mean of a sample of 100 is above 98.8? Note as n grows, SD shrinks, but only by square root of n! 21 c, d Pregnancy 23 Pregnancy skewed 22 Rainfall 24 At work 28 Potato chip bags A)Having gotten your 30 slips of paper from the green shoebox and counted how many 1's you have--Calculate the proportion of 1's, p-hat, for your sample. Also plug in p-hat (instead of p) to the formula for SD(p-hat): so if you got 12/30, p-hat = .4. "q-hat" = 1 - p-hat = 1-.4 = .6. SD formula: square root of (p ·q/n)= square root of (.4 ·.6/30) = square root of .008 = .089 Bring these estimates of p and SD(p-hat) to class next time. (Shoebox is outside my door if you still need to do it.) |
Read,
to discuss |
Optional |
Homework questions? Day 28
Sampling DistributionsCh.
18 Details:
Day 27 and
Day 28
Take a Sample from a population. SRS!.
Imagine (simulate) what would happen if you
took "all possible" SRS's. For each sample, calculate a
statistic.
Take n independently sampled values from a population with population
proportion p:
Sampling distribution of sample proportion p-hat
(read: p-hats from all possible samples) is well modeled by N(p, 
)
if np & nq are >10 (at least 10 successes and
10 failures expected), and n < 10% of population.
Sampling distribution of the mean,
y-bar: Day 28
Distribution of all means from all possible random samples of size
n from a population.
Need Random Sample, Independence (in particular,
for sampling without replacement, n < 10% of population.)
Population has mean µ and
standard deviation 
.
Whatever
the shape of the population distribution that we draw the sample
from, 
IF the population is Normal,the
sampling distribution of the y-bars is Normal.
The Central
Limit Theorem (CLT) In
any case, for "large" n, the sampling distribution of the y-bars is
Approximately Normal.
Start here Friday:
Average of Spinners, Day 28
New on this page:
How large is "large"? How approximate is
"approximate"?
If the population was close
to normal, n doesn't need to be very large.
Even if the population is
pretty weird, n=25 gives a pretty good approximation to normal.
But if we have really Big outliers or really BAD skewness, many need much
more.
Pictures on overhead.
Moore applet, Central Limit theorem
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