Chapter
12: Inference for Proportion

12.1 Inference for a Population
Proportion (pp. 684-698)

1.
In statistics,
what is meant by a *sample proportion*? The statistic that
estimates the parameter *p* is the
sample proportion _{}

2.
Give the mean and
standard deviation for the sampling distribution of _{}?

The mean is *p*
and the standard deviation is _{}

3.
How do you
calculate the standard error of _{}? The standard error of _{}is _{}

4.
What assumptions
must be met in order to use *z procedures*
for inference about a proportion?

SRS

n £ 10% of population

For a hypothesis test of *H _{0} : p = p_{0}*, the
sample size

both

For a confidence interval, the sample size

both

5.
Describe how to
construct a level C confidence interval for a population proportion. Draw a SRS of size n
from a large population with unknown proportion *p* of successes. An
approximate level C confidence interval for *p*
is _{}where z* is the upper _{}standard normal critical value.

6.
For a one-sample
hypothesis test where _{}, what is the z test statistic?

_{}

7.
What formula is
used to determine the sample size necessary for a given margin of error?

Solving the
formula
_{} for *n*,
yields _{}, where *p** is a guessed value for the sample proportion _{} and z* is the standard normal critical point
for the level of confidence you want. If
you use *p** = 0.5 in this formula, the
margin of error of the interval will be less than or equal to *m* no matter what the value of _{}is.

12.2 Comparing Two Proportions (pp.
702-719)

1. Give
the mean and standard deviation for the sampling model of _{}.

The mean of _{} is _{}

The standard deviation is _{}

2.
How do you
calculate the standard error of _{}?

_{}

3.
What assumptions
must be met in order to use *z procedures*
for inference about two proportions?

You need a SRS of size *n _{1}* from a population having proportion

The population must be at least 10 times as large as the sample and

4.
Describe how to
construct a level C confidence interval for the difference between two
proportions, _{}. An approximate level
C confidence interval for _{} is

_{} where _{} and z* is the upper _{}standard normal critical value.

5.
For a two-sample
hypothesis test where _{}, what is the z test statistic? What are the conditions for using this
statistic?

_{}

Conditions: SRS

n £ 10% of population

independently chosen samples

_{}