For each of the following tables, calculate the obtained chi square. (Hint: Calculate the expected frequencies for each cell with Formula 10.2. Double- check to make sure you are using the correct row and column marginals for each cell. It may be helpful to record the expected frequencies in table format; see Tables 10.2 10.4, and 10.8. Next, use a computational table to organize the calculation for Formula 10.1; see Tables 10.5 and 10.9. For each cell, subtract expected frequency from observed frequency and then record the result in column 3. Square the value in column 3 and then record the result in column 4. Divide the value in column 4 by the expected frequency for that cell and then record the result in column 5. Remember that the sum of column 5 in the computational table is obtained chi square. As you proceed, double-check to make sure you are using the correct values for each cell.)

a. 20 25 45

    25 20 45

    45 45 90 

b. 10 15 25

    20 30 50

    30 45 75 

c. 25 15 40

    30 30 60

  55 45 100

d. 20 45 65

    15 20 35

  35 65 100