Answer: (a). insufficient evidence.
(b). sufficient evidence
(c). insufficient evidence
Step-by-step explanation:
we will analyse this carefully to help us understand it better.
we have the standard deviation for the original suit = 2mm
standard deviation for new suit = 1.6mm
given n = 1.6
from the question we know that the suit with less standard deviation is better than the other suit
considering a null hypothesis;
H₀ : б ≥ 2, (here the new suit is not better than the original alternative hypothesis).
Also Hi : б < 2 (we have here that the new suit is better than the original )
using the Chi-Square distribution with n-1 degree of freedom to test the claim about the value of the standard deviation;
X² = (n-1) s²/ б² = (16-1)(1.6)² / (2)² = 9.6
taking the P value of X² (9.6) for 15 D O F from the P value table gives us
1-0.8441 = 0.1559
also ∝ = 0.05
where P-value > ∝ (0.05)
we can see from here that there is insufficient evidence to claim that new suit is better than that of the original suit, having failed to neglect H₀
(b). Given n = 100 and s = 1.6
then we have that X² = (n-1) s²/ б² = (100-1)(1.6)² / (2)² = 63.36
P-value of X² at 99 dif gives 0.0020
where ∝ = 0.05
since P value < ∝
rejecting the null hypothesis H₀,
we can safely say that there is sufficient claim that the new suit is better than the original at 95%.
(c). where we have that ∝ = 0.001
for part(b) P-values = 0.0020
given P-value > ∝ ;
we fail to neglect the null hypothesis.
From this we can say that the is insufficient evidence backing the claim thhat the new suit is better than the original suit at 99.99% confidence level.
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