A study was conducted in which the teachers were asked to rate students for a particular trait on a ten point scale. With the help of data given below. Find out whether significant difference exist in the rating of the student by the teacher.

A B C D E F G
X 7 3 7 1 5 5 5
Y 5 5 9 4 3 5 4
Z6 3 7 1 3 5 3

Use the Chi-square (X^2) method.

X^2 = ∑ (O-E)^2/E, where O = observed frequency and E = expected frequency.

∑ = sum of all the cells.

E = (column total * row total)/grand total

df = n - 1, where n = number of cells

Look up value in X^2 table in the back of your textbook.