a) The critical values of the ◊◊◊Distribution table are needed for the given data. They are given below:
| P | |||||||||
| df | 0.995 | 0.975 | 0.9 | 0.5 | 0.1 | 0.05 | 0.025 | 0.01 | 0.005 |
| 9 | 1.735 | 2.700 | 4.168 | 8.343 | 14.684 | 16.919 | 19.023 | 21.666 | 23.589 |
When ◊◊◊is calculated to be 17 and the df as 9, according to the above table, since the value of 17 lies between the values of 16.919 and 19.023, the approximate probability value will be between the corresponding P values of 0.05 and 0.025. Hence the approximate probability value would be between 0.05 and 0.025.
b) The values for the second set of data can be obtained from the table of critical values of the ◊◊◊distribution table.
| P | |||||||||
| df | 0.995 | 0.975 | 0.9 | 0.5 | 0.1 | 0.05 | 0.025 | 0.01 | 0.005 |
| 6 | 0.676 | 1.237 | 2.204 | 5.348 | 10.645 | 12.592 | 14.449 | 16.812 | 18.548 |
When ◊◊◊is calculated as 17 and the df as 6, according to the above table, the value of 17 lies between the values of 16.812 and 18.548. The corresponding probability value P is between 0.01 and 0.005.
c) The rule or trend which can be observed in the previous two calculations is the effect of df values on the probability values. The probability values indicate whether that the given hypothesis can be rejected or accepted.
In the first set of data, the P value is between the values of 0.05 and 0.025. This indicates that since the P value is not above the cut-off value of 0.05, the results might not be compatible with the hypothesis.
In the second set of data, the P value is 0.01 which is less than the cut-off value of 0.05. Hence we can reject the second hypothesis.
Hence the lower the df value, the greater the chances of rejecting the hypothesis.