Chapter 13: Inference for Tables

Key Vocabulary:

§ chi-square test for goodness of fit

§ segmented bar chart

§ chi-square statistic

§ expected count

§ observed count

§ degrees of freedom

§ chi-square distribution

§ components of chi-square

§ cell counts

§ r x c table

§ cell

Calculator Skills:

§ sum ( )

§
c^{2}cdf
(leftbound, rightbound, df)

§
c^{2}pdf
(X, df)

§
Shade
c^{2}
(leftbound, rightbound, df)

§
c^{2}-Test

13.1 Test for Goodness of Fit (pp.728-744)

1.
What information does a *segmented bar chart* show?

2.
Explain how to construct a *segmented bar chart*. Draw a sketch.

3.
What is the *chi-square statistic*?

4.
What is the difference between the notation X^{2} and
c^{2}?

5.
How many degrees of freedom does the *chi-square distribution *
have?

6.
As the *chi-square statistic* increases, what happens to the
P-value?

7.
What is the domain of a *chi-square distribution*?

8.
What is the shape of a *chi-square distribution*? What happens to
the shape as the degrees of freedom increases?

9.
State the null and alternative hypotheses for the *goodness of fit test*.

10.
What conditions must be met in order to use the *goodness of fit test*?

11.
What is meant by a *component* of chi-square?

12.
What does the largest *component* of chi-square signify?

13.2
Inference for Two-Way Tables (pp.744-775)

1. Why is it necessary to perform follow-up analysis to a chi-square test?

2. What information is contained in a two-way table for a chi-square test?

3. State the null and alternative hypotheses for comparing more than two proportions.

4. How do you calculate the expected count in any cell of a two-way table when the null hypothesis is true?

5. How many degrees of freedom does a chi-square test for a two-way table with r rows and c columns have?

6. If you have an entire population, or a single SRS, with each individual classified according to both of two categorical variables, what is the null hypothesis for a chi-square test?