Hypothesis Testing for a Proportion
Submitted by gfj100 on Wed, 11/11/2009  13:15
Ultimately we will measure statistics (e.g. sample proportions and sample means) and use them
to draw conclusions about unknown parameters (e.g. population proportion and population
mean). This process, using statistics to make judgments or decisions regarding population
parameters is called statistical inference.
Example 2 above produced a sample proportion of 47% heads and is written:
[read phat] = 47/100 = 0.47
Phat is called the sample proportion and remember it is a statistic (soon we will look at sample
means,
.) But how can phat be an accurate measure of p, the population parameter, when
another sample of 100 coin flips could produce 53 heads? And for that matter we only did 100
coin flips out of an uncountable possible total!
The fact that these samples will vary in repeated random sampling taken at the same time is
referred to as sampling variability. The reason sampling variability is acceptable is that if we
took many samples of 100 coin flips an calculated the proportion of heads in each sample then
constructed a histogram or boxplot of the sample proportions, the resulting shape would look
normal (i.e. bellshaped) with a mean of 50%.
[The reason we selected a simple coin flip as an example is that the concepts just discussed can
be difficult to grasp, especially since earlier we mentioned that rarely is the population parameter
value known. But most people accept that a coin will produce an equal number of heads as tails
when flipped many times.]
A statistical
hypothesis test
is a procedure for deciding between two possible statements about a
population. The phrase
significance test
means the same thing as the phrase "hypothesis test."
The two competing statements
about a population
are called the null hypothesis and the
alternative hypothesis.
•
A typical
null hypothesis
is a statement that two variables are not related. Other
examples are statements that there is no difference between two groups (or treatments) or
that there is no difference from an existing standard value.
•
An
alternative hypothesis
is a statement that there is a relationship between two
variables or there is a difference between two groups or there is a difference from a
previous or existing standard.
NOTATION
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 Spring '11
 AndyRegards
 Statistics, Null hypothesis, Statistical hypothesis testing

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