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Chapter 22: Comparing Two Proportions

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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).

Independent Trials (Individuals Assumption:

- Random Condition
- 10% Condition
Independent Group Assumption:

Can be assumed by looking at the way data was collected

Normal Distribution Assumption:

- Success/Failure Condition

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

Only, if we know population proportion (very unlikely)

When we don’t know population proportions (likely)

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.

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.

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

- 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.

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.

- 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.

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).