Homework Assignment Application
Problems Numbers Assigned: 10.58, 10.59, 11.36, and 12.56
Problem 10.58
A:
Black Belt:
s1 = 23,337, n1 = 147
Green Belt:
s2 = 25,503, n2 = 29
α = 0.05
Null and alternative hypothesis:
Hₒ: σ₁2 = σ₂2
H₁: σ₁2 ≠ σ₂2
Test statistic:
F = s2² / s1² = 25,503² / 23,337² = 1.1942
Degree of freedom:
df₁ = n2-1 = 28
df₂ = n1-1 = 146
P-value:
P-value = 2*F.DIST.RT(1.1942, 28, 146) = (0.246935) * 2 = 0.49387
Conclusion:
As p-value > α, we fail to reject the null hypothesis.
There is not enough evidence to conclude that there is a variability in the salaries between black
belts and green belts.
B:
we will use Two sample t test with equal variance or two independent sample pooled t test.
C:
For Black belt: x
̅1 = 96,682, s1 = 23,337, n1 = 147
For Green belt: x
̅2 = 77,514, s2 = 25,503, n2 = 29
Problem 10.59
A:
F-variance test:
DF1= n1-1 =146
DF2 = n2-1 = 28
𝐻0: 𝜎2
1=𝜎2
2
𝐻𝑎:𝜎2
1≠ 𝜎2
2
Test statistic:
𝐹 =𝑆1
2
𝑆2
2= 23337
25503 = 0.837351
P-value: 0.494
The test statistic is not significant and failed to reject H0. There is not enough evidence to
support that the difference between two variances.
B:
