σ0=240, N=8, s=300
We assume that the breaking strengths has normal distribution
a)α=0.05
H0:σ2=σ02=2402,H1:σ2≠ σ02=2402
x2=((N-1)s2)/σ02, s2 is a random value of corrected variance
This random variable has x2distribution with k=N−1=7 degree of freedom.
Observed value:x2≈10.9375.Critical values: x2crleft=x2cr(1-α/2;k)=1.6899
x2crright=x2cr(α/2;k)=16.013
Critical region(-∞;1.6899)"\\bigcup" (16.013;∞)
Our observed value does not fall into the critical region.So we accept H0 - Variability did not change after a change in the process of manufacture.
b)α=0.01
Critical values: x2crleft=x2cr(1-α/2;k)=0.9893
x2crright=x2cr(α/2;k)=20.278
Critical region(-∞;0.9893)⋃ (20.278;∞)
Our critical value does not fall into the critical region.So we accept H0 Variability did not change after a change in the process of manufacture.
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