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 statistic in each of the following circumstances: a. α=0.05, r=4 rows, c=5 columns b. α=0.01, r=4 rows, c=5 columns c. α=0.01, r=4 rows, c=6 columns d. α=0.01, r=3 rows, c=6 columns e. α=0.01, r=6 rows, c=3 columns

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 statistic in each of the following circumstances: a. α=0.05, r=4 rows, c=5 columns b. α=0.01, r=4 rows, c=5 columns c. α=0.01, r=4 rows, c=6 columns d. α=0.01, r=3 rows, c=6 columns e. α=0.01, r=6 rows, c=3 columns

Question
Two-way tables
asked 2021-03-02
When performing a \(\displaystyleχ^{{2}}\) 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:
a. α=0.05, r=4 rows, c=5 columns
b. α=0.01, r=4 rows, c=5 columns
c. α=0.01, r=4 rows, c=6 columns
d. α=0.01, r=3 rows, c=6 columns
e. α=0.01, r=6 rows, c=3 columns

Answers (1)

2021-03-03
(a) Given:
r = Number of rows in table = 4
\(\displaystyle¢\) = Number of columns in table = 5
a = Significance level = 0.05
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) = (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.
\(\displaystyle{x}^{{2}}={21.026}\)
(b) Given:
r = Number of rows in table = 4
\(\displaystyle¢\) = Number of columns in table = 5
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) = (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.
\(\displaystyle{x}^{{2}}={26.217}\)
(c) Given:
r = Number of rows in table = 4
\(\displaystyle¢\) = 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) = (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.
\(\displaystyle{x}^{{2}}={30.578}\)
(d) Given:
r = Number of rows in table = 3
\(\displaystyle¢\) = 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.
\(\displaystyle{x}^{{2}}={23.209}\)
(e) Given:
r = Number of rows in table = 6
\(\displaystyle¢\) = 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.
\(\displaystyle{x}^{{2}}={23.209}\)
a. 21.026. b. 26.217. c. 30.578. d. 23.209. e. 23.209.
0

Relevant Questions

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