AP Statistics

Notes 11.2

Chi-Square Test of Homogeneity = independent SRSs OR random assignment to treatments

Chi-Square Test of Independence = SRS from a single population (broken down into categories)

Hypotheses:
Ho: There is no difference in the distributions of ______
Ha: There is a difference in the distributions of ______
Conditions:
Random: The data come for a random sample or a randomized experiment
Large Sample Size: All expected counts are at least 5.
Independent: 10n ≤ population
Chi-square statistic:

Expected counts:

Degrees of freedom:
(# of rows – 1)(# of columns – 1)

Examples:

1.  In a study of the television viewing habits of children, a developmental psychologist selects random samples of 100 boys and 200 girls. Each child is asked which of the following TV programs they like best: Cyberchase, SpongeBob, or The Simpsons. Results are shown in the two-way table below.

Viewing Preferences / Row total
Cyberchase / SpongeBob / The Simpsons
Boys / 50 / 30 / 20 / 100
Girls / 50 / 80 / 70 / 200
Column total / 100 / 110 / 90 / 300

Do the boys' preferences for these TV programs differ significantly from the girls' preferences? Use a 0.05 level of significance.

H

A

N/T

O

M

S

2.  The 1999 National Gun Policy Survey asked respondents, “Do you think there should be a law that would ban possession of handguns except for the police and other authorized persons?” Here are the responses, broken down by the respondent’s level of education:

Level of Education / Yes / No
Less than high school / 58 / 58
High school graduate / 84 / 129
Some college / 169 / 294
College graduate / 98 / 135
Post graduate degree / 77 / 99

Does the sample provide good evidence that the proportion of the adult population who favor a ban on handguns changes with the level of education?