A principal at a small school wanted to know if the racial makeup of the school

Question

A principal at a small school wanted to know if the racial makeup of the school staff mirrored that of the student body. The student body can be broken down into the following racial composition: 31 were White, 18 were Latino, 10 were African American, and 6 were other races. Of the staff members, 42 were White, 4 were Latino, 15 were African American, and 4 were other races. Conduct a Chi-Square Test for Goodness of Fit using a .05 significance level to determine if the racial makeup of the staff members is different from that of the students.

Hint: This can be done by treating the racial composition of the students as the expected frequency while the racial composition of the staff is the observed frequency.

State the null and alternative hypotheses in words (1 point each, 2 points total)

Calculate X2 statistic (1 for formula, 1 for process, 1 for result, 3 points total)

Identify the critical value (1 point)

Compare the X2 statistic with the critical value (1 point)

Make a decision about the hypothesis test, using “reject” or “fail to reject” in the answer (1 point)

Explain the conclusion in a sentence or two (1 point)

Explanation / Answer

null hypothesis: ho:racial makeup is independent of staff and student body.

alternate hypothesis: it is dependent,

from above X2 stat =11.967

for (row-1)*(column-1)=3 degree of freedom . X2 critical value =7.814

as chi stat is greater then chi square critical, we reject null hypothesis.

and conclude that racial compostion is dfifernt b/w staff members to b/w student body.

Observed O white latino african-American Other Total student 31 18 10 6 65 staff 42 4 15 4 65 Total 73 22 25 10 130 Expected E=rowtotal*column total/grand total white latino african-American Other Total student 36.500 11.000 12.500 5.000 65 staff 36.500 11.000 12.500 5.000 65 Total 73 22 25 10 130 chi square =(O-E)^2/E white latino african-American Other Total student 0.829 4.455 0.500 0.200 5.983 staff 0.829 4.455 0.500 0.200 5.983 Total 1.658 8.909 1.000 0.400 11.967

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.