Notes pg 730769
I.
Confidence Interval for the Mean
a.
We can’t simply calculate a sample mean and assume that is equals the
mean of the population. A sample mean might equal the mean of the
population, but we can’t assume that it will.
b.
There are two different approaches to the construction of confidence
intervals for the mean
1.
One approach is used when we know the value of the population
standard deviation
2.
Another approach is used when we don’t know the value of the
population standard deviation. (This one is used more frequently)
II.
The Central Limit Theorem tells us that the standard error of the sampling
distribution will equal the standard deviation of the population divided by the
square root of our sample size.
a.
Ex: the standard deviation for the general population is 100. Thus, we
divide 100 by the square root of our sample size to get the value of the
standard error.
b.
We can obtain the standard error of the mean by dividing the standard
deviation (100) by the square root of our sample size (15). Thus : 100/15 =
6.67.
c.
With this formula, it is possible for us to miss our mark
1.
This method that we use will produce an interval that contains
the true mean of the population 99 times out of 100 (99% of the
time).
2.
If it were repeated 100 times, we’d find ourselves working with
many different sample means, which would result in different
final answers.
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 Spring '10
 Cleveland
 Normal Distribution, Standard Deviation

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