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Are the events happy-level and grade independent? a. Fill in the blanks. Write your answers in 2 decimals. Here is the frequency table (f ij
Are the events "happy-level" and "grade" independent?
a. Fill in the blanks. Write your answers in 2 decimals.
Here is the frequency table (fij)
A | B | C | D | F | Total | |
Very happy | 21 | 14 | 16 | 5 | 2 | 58 |
Happy | 12 | 7 | 21 | 9 | 1 | 50 |
Sad | 9 | 8 | 18 | 16 | 4 | 55 |
Very sad | 15 | 12 | 12 | 8 | 5 | 52 |
Total | 57 | 41 | 67 | 38 | 12 | 215 |
Here is the expected frequency table (eij)
A | B | C | D | F | |
Very happy | 15.38 | 11.06 | 18.07 | 10.25 | 3.24 |
Happy | 13.26 | 9.53 | 8.84 | 2.79 | |
Sad | 14.58 | 10.49 | 17.14 | 9.72 | 3.07 |
Very sad | 13.79 | 9.92 | 16.20 | 9.19 | 2.90 |
Here is the table for(fijeij)2eij
A | B | C | D | F | |
Very happy | 2.06 | 0.78 | 0.24 | 2.69 | 0.47 |
Happy | 0.12 | 0.67 | 0.00 | 1.15 | |
Sad | 2.14 | 0.59 | 0.04 | 4.06 | 0.28 |
Very sad | 0.11 | 0.44 | 1.09 | 0.15 | 1.52 |
b. The chi-square test statistic is 20.48, find the p -value.
Answer: p-value is between and . Write your answers in 2 decimals from small to large.
c. Can we say the events are independent?
Answer: . Write 1 for YES and 2 for NO.
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