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Class 2
Hypothesis Test for p
Hypothesis Test for --Small sample,
 unknown
Hypothesis Test for 1 - 2 (large
sample)
A Population Proportion, p
• Population is characterized by objects that
possess or do not possess some attribute.
We are interested in the proportion of the
population that has the attribute.
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Proportion of voters that will vote for a party.
Proportion of smokers that contract a disease.
Proportion of defects shipped in a manufactured lot.
Proportion of invoices which contain an error.
Proportion of consumers who will buy a product.
Proportions (cont.)
• The problem is analogous to the problem
about means.
• Here we have a population proportion, p, that we do
not know. We will take a sample and compute the
sample proportion, p . It turns out that under
repeated sampling, p has a normal distribution with
E ( p )  p, and  p 
p(1  p)
.
n
• Thus, we will be able to construct a test statistic
z

p p
.
p (1  p )
n
EXCEL and Population
Proportions
• EXCEL does not directly support the
computation that we are doing.
• Two possible approaches:
• (1) Use the z-test. The mean (X) to test is the
hypothesized value of p. The standard deviation is
your computation of  p. For a sample of size n,
put the value of p in n consecutive cells.
• (2) Use the function critbinom(n, p, ).
Tests for  when  is Unknown:
The t-test
• Situation is the same as before: we want to
test a hypothesis about a population mean.
This would lead us to use our test statistic
z 
x

.
n
• But what would we do if we don’t know ?
As you might already guess, this is the rule as opposed
to the exception. Thus, our test has wide applicability.
Doing a t-test in EXCEL
• Use tools/data analysis/t-Test: Paired Two
Sample for Means.
• Input data as normal, but input a new data
set of 0’s of the same size.
• The hypothesized difference is just the
hypothesized mean.
Comparing Two Population
Means
• Hypothesis consists of a direct comparison
(by looking at a difference) of 1 and 2.
• Directly supported by EXCEL through
tools/data analysis/z-Test:Two sample for
means.