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Chapter 20: Two Categorical Variables: The Chi-Square Test

Knowledge Prerequisites

Simple Random Sample (SRS)

1. declarative knowledge (definitions)
   1. SRS
2. procedural knowledge
   1. how to find SRS of any size from a population
3. conditional knowledge
   1. know advantages and disadvantages of SRS
4. resources
   1. Chapter 7 of text

Sampling Distribution

1. declarative knowledge (definitions)
   1. sampling distribution
2. procedural knowledge
   1. how to construct a sampling distribution
   2. how to calculate the mean of sampling distribution
   3. how to calculate the standard deviation of sampling distribution
   4. how to find the z-score given a proportion of area under a normal curve using the TI-83/84
3. conditional knowledge
   1. know difference between parameter and statistic
   2. know when a sampling distribution is needed for a given problem
4. resources
   1. Chapter 9 of text

Central Limit Theorem

1. declarative knowledge (definitions)
   1. central limit theorem (CLT)
2. procedural knowledge
3. conditional knowledge
   1. know how the 68-95-99.7 rule relates to the area under a sampling distribution
   2. know the shape of a sampling distribution
4. resources
   1. Chapter 9 of text

Two-Way Tables

1. declarative knowledge (definitions)
   1. two-way table
   2. categorical variable
2. procedural knowledge
   1. how to enter data into matrices in TI-83/84
   2. how to fill-in empty cells
3. conditional knowledge
4. resources
   1. Chapter 6 of text

Hypothesis Testing for Population Proportions

1. declarative knowledge (definitions)
   1. hypothesis test
   2. null hypothesis, $H_0$
   3. alternate hypothesis, $H_a$ or $H_1$
   4. one-sided test
   5. test-statistic
   6. p-value
   7. significance level, $\alpha$
   8. population proportion, $p$
   9. sample proportion, $\hat{p}$
2. procedural knowledge
   1. know the steps to perform a hypothesis test
   2. how to find the p-value for a hypothesis test
   3. how to make a conclusion for a hypothesis test
   4. how to find P(Type I error)
3. conditional knowledge
   1. how to use confidence intervals in hypothesis testing
4. resources
   1. Chapter 18 of text

Learning Goals

1. declarative knowledge (definitions)
   1. expected counts
   2. observed counts
   3. the chi-square test statistic, ${\chi }^2$
   4. the chi-square distribution
   5. degrees of freedom (to identify chi-square distribution)
2. procedural knowledge
   1. know the steps to perform a hypothesis test
   2. how to find the degrees of freedom for ${\chi }^2$-test
   3. how to calculate expected counts (by hand)
   4. how to calculate the value of the ${\chi }^2$-test statistic (by hand)
   5. how to perform ${\chi }^2$-test for comparing proportions with TI-83/84
3. conditional knowledge
   1. know the minimum requirements for using the ${\chi }^2$-test (see p. 545 of text).
   2. know when to use the two-sample z-test in lieu of ${\chi }^2$-test.

Questions to Ponder

1. What is the best way to study/prepare for the concepts in this section? Are there are other methods to study these concepts?
2. What questions do you need to ask the instructor?

Purpose of this Section

Resources

• TBA

General Notes

You are NOT responsible for goodness of fit.

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