When performing a χ^2 test of independent in a contingency table with r rows and c columns, determine the upper-tail critical value of the test statis
vestirme4
Answered question
2021-03-02
When performing a test of independent in a contingency table with r rows and c columns, determine the upper-tail critical value of the test statistic in each of the following circumstances:
1. α=0.05, r=4 rows, c=5 columns
2. α=0.01, r=4 rows, c=5 columns
3. α=0.01, r=4 rows, c=6 columns
4. α=0.01, r=3 rows, c=6 columns
5. α=0.01, r=6 rows, c=3 columns
Answer & Explanation
Nichole Watt
Skilled2021-03-03Added 100 answers
(1) Given:
r = Number of rows in table = 4
¢ = Number of columns in table = 5
a = Significance level = 0.05
The number of rows and columns, both decreased by 1, are multiplied by the degrees of freedom.
df = (r—1)(c— 1) = (4-1)(5-1) = 3(4) = 12
Determine the critical value in the row with df = 12 and in the column with a = 0.05 in the chi-square distribution table in the appendix.
(2) Given:
r = Number of rows in table = 4
¢ = Number of columns in table = 5
a = Significance level = 0.01
The product of the number of rows and the number of columns, both reduced by 1, is the degrees of freedom.
df = (r—1)(c— 1) = (4-1)(5-1) = 3(4) = 12
Determine the critical value in the row with df = 12 and in the column with a = 0.01 in the chi-square distribution table in the appendix.
(3) Given:
r = Number of rows in table = 4
¢ = Number of columns in table = 6
a = Significance level = 0.01
The product of the number of rows and the number of columns, both reduced by 1, is the degrees of freedom.
df = (r—1)(c— 1) = (4-1)(6-1) = 3(5) = 15
Determine the critical value in the row with df = 15 and in the column with a = 0.01 in the chi-square distribution table in the appendix.
(4) Given:
r = Number of rows in table = 3
¢ = Number of columns in table = 6
a = Significance level = 0.01
The degrees of freedom is the product of the number ofrow and the number of columns, both decreased by 1.
df = (r—1)(c— 1) = (3-1)(6-1) = 2(5) = 10
Determine the critical value in the row with df = 10 and in the column with a = 0.01 in the chi-square distribution table in the appendix.
(5) Given:
r = Number of rows in table = 6
¢ = Number of columns in table = 3
a = Significance level = 0.01
The degrees of freedom is the product of the number ofrow and the number of columns, both decreased by 1.
df = (r—1)(c— 1) = (6-1)(3-1) = 5(2) = 10
Determine the critical value in the row with df = 10 and in the column with a = 0.01 in the chi-square distribution table in the appendix.
1) 21.026. 2) 26.217. 3) 30.578. 4) 23.209. 5) 23.209.
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