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Sagot :
Answer:
1) H0 : σ₁ ²≥ σ₂²; Ha: σ₁² < σ₂²
2) χ²= 43.52
3) The critical region is χ²≤ 5.23
4) Reject the alternate hypothesis.
5) We conclude that the alternate hypothesis is false and accept the null hypothesis.
Step-by-step explanation:
The claim is that it fills bottle with a lower variation which is the alternate hypothesis
1) Ha: σ₁² < σ₂² where σ₁² is the variation of the new machine and σ₂² is the variation of the old machine.
The null hypothesis is opposite of alternate hypothesis H0 : σ₁ ²≥ σ₂²
2) The test statistic is χ²= ns²/σ ² which under H0 has χ² distribution with n-1 degrees of freedom assuming the population is normal.
The calculated χ²= ns²/σ ² = 68( 0.12)²/ (0.15)²=0.9792/0.0225= 43.52
3) The critical region is entirely in the left tail. χ²≤χ²( 0.99)(15)= 5.23
4) The alternate hypothesis is false hence reject it.
5) The calculated χ²= 43.52 does not lie in the critical region χ²≤ 5.23 therefore H0 is accepted and concluded that new machine does not fill bottles with a lower variation.
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