Testing Hypotheses About Proportions - STAT E-50...

STAT E-50 - Introduction to Statistics
Testing Hypotheses About Proportions
Hypotheses
The null hypothesis:
H
0
: parameter = hypothesized value
The alternative hypothesis:
H
a
: parameter = value we would accept if we reject the null hypothesis
Model
Specify the model you will use to test the null hypothesis
State the parameter of interest
List the assumptions and check the conditions
Name the statistical test you will use
Mechanics
Calculate a test statistic from the data
Obtain a P-value = the probability that the observed value of the test statistic (or
a more extreme value) could occur if the null model were correct
If the P-value is small enough, we will reject the null hypothesis
Conclusion
Statistical conclusion: state whether you reject or fail to reject the null hypothesis
State your conclusion in context

One-proportion z-test
H
0
: p = p
0
Test statistic is 0
ˆ
p p
z
ˆ
SD(p)
−
= where 0 0
p q
ˆ
SD (p)
n
=
When the conditions are met and the null hypothesis is true, this statistic
follows the standard Normal model.
Conditions: Independence condition
Random sampling condition
10% condition
Success/failure condition (using p
0
and q
0
)
Note: p
0
is the value you are testing in H
0
; q
0
= 1 - p
0
is the observed value of p
ˆ
p
Page 2

1. An American Demographics study conducted in 1980 found that 40% of new car
buyers were women. Suppose that in a random sample of 120 new car buyers in 2000,
57 were women. Does this indicate that the true proportion of new car buyers in 2000
who were women is significantly larger than the 1980 proportion?
Plan
What do we want to know?
What are the variables? What are the W’s?
Hypotheses
H
0
:
H
a
:
Model
Check the conditions:
Independence condition
Random sampling condition
10% condition
Success/failure condition (using p
0
and q
0
)
Specify the sampling distribution model
What test do you plan to use?