In testing the independence of two variables described in a contingency table, determine the critical value of chi-square if the test is to be conducted at the
a. á= 0.025 level and d f = 5
b. á = 0.05 level and d f = 8
c. á = 0.01 level and d f = 6
d. á = 0.10 level and d f = 4
It is the same distribution table as the other Χ² values.
For example, at α=0.025 and df=5,
look up cumulative probability of 0.975 to get 12.8.
At α=0.1 and df=6, for cumulative probability of 0.90, Χ² = 10.7.
If you do not have a Χ² table, try the calculator below:
http://stattrek.com/Tables/ChiSquare.aspx
but make sure you have access to one for your exams. Check with your teacher.
To determine the critical value of chi-square, you can use a chi-square distribution table or a statistical software. Here's how you can find the critical values for the given levels of significance (á) and degrees of freedom (df):
a. α = 0.025 level and df = 5:
First, determine the critical chi-square value for a chi-square distribution with df = 5 at the α/2 = 0.025/2 = 0.0125 level. Consulting a chi-square distribution table or using a statistical software, you can find that the critical value is approximately 11.070.
b. α = 0.05 level and df = 8:
Again, determine the critical chi-square value for a chi-square distribution with df = 8 at the α/2 = 0.05/2 = 0.025 level. Consulting a chi-square distribution table or using a statistical software, you can find that the critical value is approximately 15.507.
c. α = 0.01 level and df = 6:
To find the critical chi-square value for a chi-square distribution with df = 6 at the α/2 = 0.01/2 = 0.005 level, consult a chi-square distribution table or use a statistical software. The critical value is approximately 16.812.
d. α = 0.10 level and df = 4:
Finally, find the critical chi-square value for a chi-square distribution with df = 4 at the α/2 = 0.10/2 = 0.05 level. Consulting a chi-square distribution table or using a statistical software, you can find that the critical value is approximately 9.488.
Note: The exact critical values might differ slightly depending on the level of accuracy desired and the specific chi-square distribution table used.