Question

Find the critical values x?and XR for the given confidence level c and sample size n. C=0.8, n=30 xL= (Round to three decimal places as needed.)

Answer 1

df = 30 - 1 = 29

α = 1 - 0.8 = 0.2
The critical values for α = 0.2 and df = 29 are Χ^2(α/2,n-1) = 39.087

2)

n = 21
df = 21 - 1 = 20

α = 1 - 0.9 = 0.1
The critical values for α = 0.1 and df = 20 Χ^2(α/2,n-1) = 31.410

3)

Here s = 3.7 and n = 30
df = 30 - 1 = 29

α = 1 - 0.99 = 0.01
The critical values for α = 0.01 and df = 29 are Χ^2(1-α/2,n-1) = 13.121 and Χ^2(α/2,n-1) = 52.336

CI = (29*3.7^2/52.336 , 29*3.7^2/13.121)
CI = (7.59 , 30.26)

4)

Here s = 15 and n = 20
df = 20 - 1 = 19

α = 1 - 0.9 = 0.1
The critical values for α = 0.1 and df = 19 are Χ^2(1-α/2,n-1) = 10.117 and Χ^2(α/2,n-1) = 30.144

CI = (19*15^2/30.144 , 19*15^2/10.117)
CI = (141.8 , 422.6)

5)

Here s = 3.77 and n = 14
df = 14 - 1 = 13

α = 1 - 0.8 = 0.2
The critical values for α = 0.2 and df = 13 are Χ^2(1-α/2,n-1) = 7.042 and Χ^2(α/2,n-1) = 19.812

CI = (13*3.77^2/19.812 , 13*3.77^2/7.042)
CI = (9.33 , 26.24)

b)

Here s = 3.77 and n = 14
df = 14 - 1 = 13

α = 1 - 0.8 = 0.2
The critical values for α = 0.2 and df = 13 are Χ^2(1-α/2,n-1) = 7.042 and Χ^2(α/2,n-1) = 19.812

CI = (sqrt(13*3.77^2/19.812) , sqrt(13*3.77^2/7.042))
CI = (3.05 , 5.12)

6)

Here s = 15 and n = 20
df = 20 - 1 = 19

α = 1 - 0.9 = 0.1
The critical values for α = 0.1 and df = 19 are Χ^2(1-α/2,n-1) = 10.117 and Χ^2(α/2,n-1) = 30.144

CI = (19*15^2/30.144 , 19*15^2/10.117)
CI = (141.8 , 422.6)