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

Here chi square goodness of fit test will be used.

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The variable of interest: the racial makeup of teachers and student

The outcome variable is: The test statistics

Following table shows the calculations for expected frequency:

Following table shows the expected frequency in required format:

O p E=p*65 White 42 0.47 30.55 Latino 4 0.28 18.2 African American 15 0.15 9.75 Other 4 0.1 6.5 Total 65 65

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