You have selected a sample to use in testing a null hypothesis that Factor X and Factor Y are independent. Your job is to fill in the missing frequencies in the partially completed frequency tables below and then calculate the appropriate chi square value for the test. (For ease of calculation, round values to the nearest integer.)

OBSERVED FREQUENCIES Factor Y Y2 86 Factor X X1 X2 X3 Totals Y1 Totals 460 118 550 1000 EXPECTED FREQUENCIES Factor Y Factor X X1 X2 X3 Totals Y2 82 Y1 Totals