Question

A manager of an industrial plant asserts that workers on average do not complete a job using Method A in the same amount of time as they would using Method B. Five workers are randomly selected. The time to completion is recorded for Method A and Method B (in minutes). Is there evidence at the 5% level of Significance that Method A is faster than Method B? Method A: 12, 16, 15, 11 and 10. Method B: 6, 10, 8, 9 and 12. A. Yes, there is evidence at the 5% level of Significance that two method differ. B. No, there is no evidence at the 5% level of significance that method A is faster.

Answer 1

Method A

N₁: 5
df₁ = N - 1 = 5 - 1 = 4
M₁: 12.8
SS₁: 26.8
s²₁ = SS₁/(N - 1) = 26.8/(5-1) = 6.7


Method B

N₂: 5
df₂ = N - 1 = 5 - 1 = 4
M₂: 9
SS₂: 20
s²₂ = SS₂/(N - 1) = 20/(5-1) = 5

a) null and alternate hypothesis

H0:

H1:

b) level of significance = 0.05

c) test statistics

s²_p = ((df₁/(df₁ + df₂)) * s²₁) + ((df₂/(df₂ + df₂)) * s²₂) = ((4/8) * 6.7) + ((4/8) * 5) = 5.85

s²_M1 = s²_p/N₁ = 5.85/5 = 1.17
s²_M2 = s²_p/N₂ = 5.85/5 = 1.17

t = (M₁ - M₂)/√(s²_M1 + s²_M2) = 3.8/√2.34 = 2.48

d) p value = 0.0189

E) since p value is less than level of significance so we reject H0

So there sufficient evidence at the 5% level of significance that method A is faster.