1. Chi-Square Test
Section 12.1

2. Categorical Variables
Based on observations
Univariate – single categorical variable
Example: Sample 100 people & ask if they agree or disagree with a question.
Bivariate – uses two categorical variables
Example: Sample 100 people & ask if they are male/female and what political party they support.

3. One-Way Frequency Table - univariate
Democrat
Independent
Republican
Data
Vertical One-Way Table
Horizontal One-Way Table
Freq.
Democrat 4
Republican 6
Independent 2
Democrat
Republican
Independent
Freq. 4 6 2

4. Goodness of Fit Test
Used to measure the extent to which the observed counts differ from the expected counts.
K = # categories of a catagorical variable
Df = k – 1
Test Statistic:

5. Assumptions Observed Values are based on random Samples
Sample size is large – each cell count is at least 5.

6. Hypotheses Ho: State each proportion’s hypothesized value.
HA: At least 1 of the proportions differ from the hypothesized value.

7. It uses the Chi-Square Chart
Positively Skewed
Uses d.f.
On calculator!

8. Is there a preference in type of car?
Freq.
Expected
SUV 27
Truck 25
Sedan 29
Sports 19
P1=proportion who prefer a SUV
P2=proportion who prefer a truck
p3=proportion who prefer a sedan
P4=proportion who prefer a sports car
Assumptions: Random Samples & all cell counts are at least 5.
Use a Chi-Square goodness of fit Test
P-val = xcdf(2.24,∞, 3)=0.52

9. A researcher believes that the number of homicides crimes in CA by season is uniformly distributed. To test this claim, you randomly select 1200 homicides from a recent year and record the season when each happened.
Season
Freq
Spring
312
Summer
299
Fall
297
Winter
293

10. Results from a previous survey asking people who go to movies at least once a month are shown in the table below. To determine whether this distribution is still the same, you randomly select 1000 people who go to movies at least once a month and record the age of each. Are the distributions the same?
Age
Survey
Freq
2 - 17
26.70%
240
19.80%
214
19.70%
183
14%
156
50+
207

11. Homework
Worksheet