Answer:
a) The null hypothesis is H₀ : µ₁ ≥ µ₂
The alternative hypothesis is Hₐ : µ₁ ≤ µ₂ (left tailed)
b) using t-test, t= -2.69
c) the p-value = 0.0041
Step-by-step explanation:
Testing if the machine 2 is faster than the machine 1 is tested under the null and alternative hypothesis at a 5% level of significance.
For machine 1
Mean (µ₁)= 73.8
Standard deviation (σ₁) = 5.2
n₁ = 60
For machine 2
Mean (µ₂)= 76.1
Standard deviation (σ₂) = 541
n₂ = 60
a) The null hypothesis is H₀ : µ₁ ≥ µ₂
The alternative hypothesis is Hₐ : µ₁ ≤ µ₂ (left tailed)
b) Using t-test
t = (µ₁ - µ₂) / √ (σ₁^2/ n₁) + (σ₂^2/ n₂)
t= (73.8 – 76.1) / √ (5.2^2/ 60 )+ (4.1^2/ 60)
t= (-2.31) / √0.7309
t= -2.31/ 0.8549
t= -2.69
c) The excel function for the p-value = TDIST (2.69, 118, 1)
P-value = 0.0041
Since the p-value is less than the 5% significance level, we reject the null hypothesis.
The then conclude that machine 2 is faster than machine 1
