16. In a particular county, a random sample of 225 adults are asked for their preferences 16.

among three individuals who wish to be the state’s next commissioner of education.

Respondents also are asked to report their annual household income. The results:

Candidate Household Income Jadallah Yung Pandiscio Less than $20,000 8 11 6

$20,000–$39,999 23 17 18

$40,000–$59,999 20 22 20

$60,000 or more 25 33 22

(a) Stated very generally, what is the null hypothesis of independence in this situation?

(b) Determine fo and fe for each of the 12 cells of this 3 × 4 contingency table. Present this information in a 3 × 4 table that includes row totals, column totals, and the grand total. (For each row, does Σfe frow?)

(c) Compute χ2 (using Formula [18.1]) and complete the test at α 05.

(d) What is your general conclusion from this χ2

?