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 (Asian, Native American, etc.). Of the 65 teachers, 42 were White, 4 were Latino, 15 were African American, and 4 were denoted as Other. Do these results suggest that the racial makeup of the faculty members is different from that of the students? Carry out a chi square for goodness of fit

(Use the .05 significance level.)

What is the expected frequency for the Latino category?

In the study above, what is the value of X²?

In the study above, what is the cutoff?

Please show work provided and detailed explanation