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

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 broke 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.

a) Conduct a Chi-Square Test for Goodness of Fit to determine if the racial makeup of the staff members is different from that of the students. This can be done by treating the racial composition of the students as the expected frequency for the observed frequency of the racial composition of the staff. (Use a .05 significance level and make sure you show all 5 steps of the hypothesis test)

Solution

Step 1. Hypothesis for Teachers\' Races

H0: p1=31/65, p2 = 18/65, p3 = 10/65, p4= 6/65

H1: Not H0

Step 2. Test Statistic

Teachers Expected Values: W: 36, L:18, AA:10, OR:6

Teachers Observed Values: W: 42,L:4,AA:15,OR:4

   \\(\\chi ^{2} = \\sum \\frac{(observed-expected)^2}{expected} = 15.829\\)   

Step 3. P Value

If you look up this value along with the degrees of freedom (3) in a chi-square table, you will get a p-value of 0.001.

Step 4. Decision

Since p < 0.05, we will reject the null hypothesis.

Step 5. Explanation

The evidence suggests that the racial makeup of the teachers\' population is not the same as the students\'.