For Exercises 5–10, the observed frequencies are provided in a contingency table of two categorical variables. Find the expected frequencies, on the assumption that the variables are independent.
9.
| I1 | I2 | I3 | |
|---|---|---|---|
| J1 | 100 | 90 | 105 |
| J2 | 50 | 60 | 55 |
| J3 | 25 | 15 | 20 |
11.2.9
| I1 | I2 | I3 | Total | |
|---|---|---|---|---|
| J1 | 99.2788 | 93.6058 | 102.1154 | 295 |
| J2 | 55.5288 | 52.3558 | 57.1154 | 165 |
| J3 | 20.1923 | 19.0385 | 20.7692 | 60 |
| Total | 174.9999 | 165.0001 | 180 | 520 |