Hypothesis Testing for a Mean
Submitted by gfj100 on Wed, 11/11/2009  13:16
Quantitative Response Variables and Means
We usually summarize a
quantitative
variable by examining the mean value. We
summarize
categorical
variables by considering the proportion (or percent) in each category.
Thus we use the methods described in this handout when the response variable is quantitative.
Again, examples of quantitative variables are height, weight, blood pressure, pulse rate, and so
on.
Null and Alternative Hypotheses for a Mean
•
For one population mean, a typical null hypothesis is
H
0
: population mean μ = a specified
value. We'll actual give a number where it says "a specified value," and for paired data
the null hypothesis would be
H
0
: u
d
= a specified value. Typically when considering
differences this specified value is zero
•
The alternative hypothesis might either be onesided ( a specific direction of inequality is
given) or twosided ( a not equal statement).
Test Statistics
The test statistic for examining hypotheses about
one population mean
:
where
the observed sample mean, μ
0
= value specified in null hypothesis, s = standard
deviation of the sample measurements and n = the number of differences.
Notice that the top part of the statistic is the difference between the sample mean and the null
hypothesis. The bottom part of the calculation is the standard error of the mean.
It is a convention that a test using a tstatistic is called a ttest. That is, hypothesis tests using the
above would be referred to as "1sample t test".
Finding the pvalue
Recall that a
p
value
is the probability that the test statistic would "lean" as much (or more)
toward the alternative hypothesis as it does if the real truth is the null hypothesis.
When testing hypotheses about a mean or mean difference, a
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 Spring '11
 AndyRegards
 Statistics, Normal Distribution, Null hypothesis, Statistical hypothesis testing

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