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CHAPTER 11
Estimating Means with Confidence
Review of Ch 9 information we will use in Ch 10:
One Mean – one quantitative variable
If the population is normal or n≥30 then the
x
’s can be described as:
the shape is approximately normal
the mean is μ
the standard deviation is
n
σ
the standard error is
n
s
Mean of Paired Differences – two dependent quantitative
variables
If the population of differences is normal or n≥30 then the
d
’s can
be described as:
the shape is approximately normal
the mean is μ
d
the standard deviation is
n
d
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n
s
d
Two Independent Means – one quantitative variable and one
categorical variable with two independent groups
If both populations are normal or have n≥30 then the
2
1
x
x

’s can be
described as:
the shape is approximately normal
the mean is μ
1
 μ
2
the standard deviation is
2
2
2
1
2
1
n
n
σ
+
the standard error is
2
2
2
1
2
1
n
s
n
s
+
Confidence intervals have the general form:
Sample estimate ± Margin of error
OR
Sample estimate ± Multiplier * Standard Error
Multiplier values:
When dealing with quantitative data, we use a tmultiplier (as
opposed to the zmultiplier we used with a proportion).
Why?
The shape of quantitative data is not always normal, but as the
sample size increases, the distribution of the sample mean (xbar)
becomes more bellshaped. Because of this, when computing a CI for
quantitative data, we need a multiplier that reflects sample size (n).
In the tdistribution, sample size is reflected in the degrees of
freedom: df=n1.
So t* is a better multiplier for a CI for means than
z* would be.
How do we determine the t* multiplier
?
The table is located before the ztable in the back cover of the
textbook; labeled
t* Multipliers for CIs and Rejection Region
Critical Values,
also table A.2 in the text, page 728.
To use the t* multiplier table we need to know
the
confidence level
and the
sample size.
For example, suppose we want a 95% C.I. for the population mean
using a sample of size n=13. Our degrees of freedom would be df =
n1 = 13 – 1 = 12. So, to find the multiplier we would look across the
df = 12 row and down the .95 confidence level column. We find that
our t* multiplier is 2.18.
As the sample size increases the standard error and the t* multiplier
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This note was uploaded on 03/30/2008 for the course L I R 201 taught by Professor Willits,billie during the Spring '07 term at Pennsylvania State University, University Park.
 Spring '07
 WILLITS,BILLIE

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