Chapter 22: Comparing Two Proportions

AP Statistics

In this chapter, we take what we have learned and apply it to comparing two proportions and determining if there is a difference between the two proportions (obtained from two samples).

Assumptions and Conditions for Two-Proportion z-interval and Two-

Proportion z-testIndependent Trials (Individuals Assumption:

Random Condition10% Condition

Independent Group Assumption:Can be assumed by looking at the way data

was collected

Normal Distribution Assumption:Success/Failure Condition

Sampling Distribution Model for a Difference Between Two-Independent Proportions

Only, if we know population proportion (very unlikely)

How we make our sampling model (Normal Model)—may need to use SE

How To Determine a Two-Proportion z-Interval

When we don’t know population proportions (likely)

Example

A magazine article surveyed 12,460 males and 12,678 females to see if they had finished high school (all aged 24). 84.9% of males and 88.1 females reported “yes”. Create a 95% confidence interval for the difference in graduation rates between males and females and interpret it in context.

Example

Two-Proportion z-Test

Typically, we start off with our null hypothesis stating that there is NO difference between the two groups.

Remember, the null hypothesis basically says that nothing is going on.

Two-Proportion z-Test

Our Null Hypothesis, typically looks like (but in context for subscripts):

Pooled Data

• Since we assume that the difference in proportions is zero, we are therefore saying that the two proportions are assumed to be EQUAL.

• If the two proportions are assumed to be equal, then we also assume that their standard errors are also EQUAL.

Pooled Data

In order to calculate what that equal proportion is, we combine the data (pool the data) to get one overall proportion.

That pooled proportion is then used to find the standard error,

Make sure “successes” are whole numbers.

Two-Proportion z-Test

Other Things

• When checking “Success/Failure Condition” you should be checking four different situations.

• CHECK assumptions/conditions and NEVER use two-proportion method if they are not satisfied.

• Same method as with one-proportion z-test.• Use the calculator (STAT TESTS)• Be careful with the alternative hypothesis.

Example

Is there a difference between the proportion of males and females who have graduated from high school? Perform a 2-proportion z-test. (Remember, you have already satisfied the conditions necessary to proceed).

Try pg 510, #20