A teacher figures that final grades in the chemistry departm

A teacher figures that final grades in the chemistry department are distributed as: A, 25%; B, 25%; C, 40%; D, 5%; F, 5%. At the end of a randomly selected semester, the following number of grades were recorded. Calculate the chi-square test statistic x^2 to determine if the grade distribution for the department is different than expected. Use a = 0.01. Grade A B C D F Numb 36 42 60 8 14

Solution

total number of students

test static = sum of (observed -Expecetd /expected)ˆ2

= (36 - 40 /40)ˆ2 + (42 - 40/40)ˆ2 + (60 - 96/96)ˆ2 + (8-8 / 8)ˆ2 + (14-8 / 8)ˆ2

= 0.01 + 0.0025 + 0.0000140625 + 0.5625

= 0.5750

critical value = 0.2971

yes grade distribution is different than expected