We want to investigate the diameter of steel rods that are manufactured on two different sites. We pick two different random samples of sizes n1 = n2 = 15. The sample means are X1 = 6.2, X2 = 7.8, respectively. The sample variances are s 2 1 = 4 and s 2 2 = 6.25. Assume that both sites produce rods of diameter that is normally distributed with the same standard deviation σ1 = σ2. Answer the following questions.
(a) Use α = 0.05 to accept or reject the hypothesis that both sites produce the same diameter rods.
(b) Assume that the two sites are unsure about whether their standard deviations are actually the same. Using the data in the exercise and assuming α = 0.05, should you accept or reject the hypothesis that both sites have the same standard deviation?
Theory:
For,
So
Sp= 2.26
t= (6.2-7.8)/(2.26*0.365)
=-1.686
P Value Results
t=-1.686 DF=28
The two-tailed P value equals 0.1029
So We reject the Null Hypothesis at alfa=0.05.
Theory:
For,
So
SΔ= 1.9159
t= (6.2-7.8)/ 1.9159
=-0.835117
P Value Results
t=-0.835117 DF=23.82
The two-tailed P value equals
0.4119
So We reject the Null Hypothesis at alfa=0.05
We want to investigate the diameter of steel rods that are manufactured on two different sites....
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