A high school principal wanted to know if the racial makeup of her teachers mirr

Question

A high school principal wanted to know if the racial makeup of her teachers mirrored that of the student body. The student body broke down into 47% White, 28% Latino, 15% African American, and 10% other. Of the 65 teachers, 42 were White, 4 were Latino, 15 were African American, and 4 were Other. How would you test this question (with what hypothesis testing procedure)? What is the variable of interest? What is the outcome variable? Draw a table showing the observed (expected) make-up of the teachers. Convert percentages to raw scores. hint: Observed (Expected) means you should report the Observed frequencies AND the expected frequencies in parentheses

Explanation / Answer

step1: Question: Is the racial makeup of the faculty members different from that of the students?

Step 2:

Null hypothesis: = equal to 100%

Alternative Hypothesis: not equal to 100%, alpha = .05

Step 3: Calculate:

Total teachers = 65

So, % for White = (42/65)*100 = 65%
% for Latino = (4/65)*100 = 6%

% for African American = (15/65)*100 = 23%

% for Other = (4/65)*100 = 6%

For a total of 100%

Step 4: Probability: 100%, all teachers reported, and student numbers are given

Step 5: Conclusion

Now, line up the numbers

Results:

White: Student = 47%, Teacher = 65%

Latino: Student = 28%, Teacher = 6%

African American: Student = 15%, Teacher = 23%

Other: Student = 10, Teacher = 6%

conclusion:The racial makeup of the staff does not mirror that of the students

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