(Lesson 29.5: Inferences from Two Samples; Ch.9)
9.01
CHAPTER 9:
INFERENCES FROM TWO SAMPLES
(LESSON 29.5)
Only Part A of this Lesson is fair for your Final.
PART A: MEANS FROM DEPENDENT SAMPLES: MATCHED PAIRS
(SECTION 94)
A matched pair
of data values may correspond to two different measures for one
individual (as in Example 1 below), the same measures for a husband/wife couple,
etc.
When comparing the means for the two measures, we perform our usual tests on
the
differences
(
d
) between the measures for each matched pair.
The population data
Let
D
be the distribution of the population of differences between all the
matched pairs.
Let
μ
d
be the mean of the
D
distribution.
The sample data
Let
d
and
s
d
be the sample mean and the sample standard deviation,
respectively, for the differences between the paired sample data values.
Let
n
be the number of matched pairs of sample data values.
CLT Assumptions
:
We require:
•
n
>
30
, or
•
D
is approximately normally distributed.
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9.02
Example 1
We take a random sample of three men from the participants in a men’s
weight loss program. Use the sample data below to test the claim that
participants in the program lose weight on average. Use a significance level
of 0.05. Assume that the weight changes of the participants in the program
are approximately normally distributed.
Subject #
Before Weight
(lbs.)
After Weight
(lbs.)
1
230
225
2
250
248
3
210
211
Solution to Example 1
We calculate the differences,
d
, from the given table.
Subject #
Before Weight
(lbs.)
After Weight
(lbs.)
Differences
(
d
in lbs.)
1
230
225
5
2
250
248
2
3
210
211
±
1
Here, we take differences “Before” – “After.” More on this later.
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 Spring '11
 staff
 Statistics, Normal Distribution, Standard Deviation, Variance, test statistic formula

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