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.