Question

Give the rejection region for a chi-square test of specified probabilities if the experiment involves k categories in these cases. (Round your answers to three decimal places.)

(a)    k = 6, α = 0.05
Χ² >  

(b)    k = 13, α = 0.01
Χ² >  

(c)    k = 17, α = 0.005
Χ² >  

(d)    k = 3, α = 0.01
Χ² >

Answer 1

Part a

We are given

k = 6

df = k – 1 = 6 – 1 = 5

α = 0.05

χ2Critical = 11.0705

Rejection region: χ2 > 11.071

Part b

We are given

k = 13

df = k – 1 = 13 – 1 = 12

α = 0.01

χ2Critical = 26.21697

Rejection region: χ2 > 26.217

Part c

We are given

k = 17

df = k – 1 = 17 – 1 = 16

α = 0.005

χ2Critical = 34.26719

Rejection region: χ2 > 34.267

Part d

We are given

k = 3

df = k – 1 = 3 – 1 = 2

α = 0.01

χ2Critical = 9.21034

Rejection region: χ2 > 9.210

[Critical values can be calculated by using Chi-square table, Excel, Ti-83/84 calculator, or statistical software’s.]