Question

When performing a χ2 test for independence 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=6​, c=5		d. α=​0.01, r=5​, c=6
b. α=​0.01, r=3​, c=4		e. α=​0.01, r=4​, c=5

c.

α=​0.01,

r=3​,

c=6

a. The critical value is ____. ​(Round to three decimal places as​ needed.)

b. The critical value is _____. ​(Round to three decimal places as​ needed.)

c. The critical value is ______. ​(Round to three decimal places as​ needed.)

d. The critical value is ______. ​(Round to three decimal places as​ needed.)

e. The critical value is _____. ​(Round to three decimal places as​ needed.)

Answer 1

a) Given that, α=​0.05, r=6​, c=5

Here, degrees of freedom = (r - 1) * (c -1)

=> DF = (6 - 1) * (5 - 1) = 5 * 4 = 20

Therefore, crtical value at,  α=​0.05 with df = 20 is, 31.410

The critical value = 31.410

b) Given that, α=​0.01, r=3​, c=4

Here, degrees of freedom = (r - 1) * (c -1)

=> DF = (3 - 1) * (4 - 1) = 2 * 3= 6

Therefore, crtical value at,  α=​0.01 with df = 6 is, 16.812

The critical value = 16.812

c) Given that, α=​0.01, r=3​, c=6

Here, degrees of freedom = (r - 1) * (c -1)

=> DF = (3 - 1) * (6 - 1) = 2 * 5 = 10

Therefore, crtical value at,  α=​0.01 with df = 10 is, 23.209

The critical value = 23.209

d) Given that, α=​0.01, r=5, c=6

Here, degrees of freedom = (r - 1) * (c -1)

=> DF = (5 - 1) * (6 - 1) = 4 * 5 = 20

Therefore, crtical value at,  α=​0.01 with df = 20 is, 37.566

The critical value = 37.566

e) Given that, α=​0.01, r=4​, c=5

Here, degrees of freedom = (r - 1) * (c -1)

=> DF = (4 - 1) * (5 - 1) = 3 * 4 = 12

Therefore, crtical value at,  α=​0.01 with df = 12 is, 26.217

The critical value = 26.217