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 H0 : p = p0, the sample size n is so large that
both np0
10 and n(1 - p0) 10
For a confidence interval, the sample size n is so large that
both and

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 n1 from a population having proportion p1 of successes and an independent SRS of size n2 from a population having proportion p2 of successes.
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