Homework SourseAssume event A is grade 80 event B is interesting class if y
Assume event A is grade 80, event B is interesting class, if you are given the following contingency table. Even A and Event B are independent or dependent? The values in the table are number of students. Pick One: Independent ( ? ) or Dependent [ ( ? )
Grade
interested
not interested
Total
lower than 80
10
20
30
greater or equal to 80
40
10
50
Total
50
30
80
| Grade | interested | not interested | Total |
| lower than 80 | 10 | 20 | 30 |
| greater or equal to 80 | 40 | 10 | 50 |
| Total | 50 | 30 | 80 |
Solution
Under null hypothesis Ho:event A is independent of event B. H1:event A is dependent of event B.
So we use chi-square independence of attribute test, so at 0.05 with (2-1)(2-1)=1 degrees of freedom is 3.841.
Then chi-squarecal=[(Oi-Ei)2/Ei]=17.4222. Here chi-squarecal>chi-squaretab, so we reject null hypothesis. Therefore, we accept H1:event A is dependent of event B.
| Oi | Ei | (Oi-Ei)2/Ei |
| 10 | (30*50)/80=18.75 | 4.0833 |
| 20 | (30*30)/80=11.25 | 6.8056 |
| 40 | (50*50)/80=31.25 | 2.4500 |
| 10 | (50*30)/80=18.75 | 4.0834 |
| 80 | 80 | 17.4222 |
