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BA 253: Business Statistics
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Finish ICE 4
Weds
Ch 7: Sampling Distributions
Start ICE 5
9/26/12
Fri
ICE 5
↑ Descriptive Statistics: Summarize Data ↑
↓ Inferential Statistics: Estimate Population from Sample ↓
Chapter 7: Sampling and Sampling Distributions
Ex:
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Collect n data, calculate sample mean = x = point estimate.
Use simple random sample.
Is x ≈ μ??? That is the question!
The approximation gets better as the sample size, n, increases.
How is x distributed? In other words, what is the probability distribution of the
sample mean? Guess = _________________
Central Limit Theorem
For large sample sizes (typically, n ≥ 30), the sample mean x is approximately normally
distributed.
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CLT is true regardless of the original distribution of the data.
As n↑, the standard deviation decreases. (That is, x gets closer to μ.)
This is why the normal distribution is so common and so important.
Show “CLT in Action”
Sampling Distribution of x
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The sample mean, x , has mean μ, standard deviation
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and is
n
o Normally distributed if the underlying distribution is Normal.
o Approximately Normally Distributed whatever the underlying
distribution is if n ≥ 30.
o As the sample size increases, n ↑, the sample mean gets closer and closer
to the population mean, x ≈ μ.
Ex: Normal with mean 100 and sd 20.
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ICE 5
Do on TI-83. Math, PRB, randNorm(100,20) – try it! 132, 104, 98, 137, 81, etc.
How close is your result to 100? Is one data point enough? No.
Get 5 numbers, then average. Closer.
On Excel, get 30, 100, 1000 numbers and then average.
As sample size increases, the approximation gets better.