Question

Are both Ho and H1 are sigma > 1.2cm? It says exceeds 1.2 cm, which means that both are sigma > 1.2cm. Confused on why we would test two of the same thing. Thanks.

A company produces metal pipes of a standard length, and claims that the standard deviation of the length is exceeds 1.2 cm. One of its clients decides to test this claim by taking a sample of 25 pipes and checking their lengths. They found that the standard deviation of the sample is 1.5 cm. Does this undermine the company's claim? Confidence level is 95% (Confidence level(%)= 100(%) - significance level(%))

Answer 1

To Test :-

H0 :-  

144 = ده

H1 :-  

0?> 1.44

Test Statistic :-

χ² = ( ( 25-1 ) * 2.25 ) / 1.44
χ² = 37.5

x = ((n − 1)2)/04

Test Criteria :-
Reject null hypothesis if
> xan-1


X0.05,25-1
= 36.415

>> 05, 25-1
= 37.5 > 36.415 , hence we reject the null hypothesis
Conclusion :- We Reject H0

Decision based on P value
P value = P ( χ² > 37.5 ) = 0.039
Reject null hypothesis if P value < α = 0.05
Since P value = 0.039 < 0.05, hence we reject the null hypothesis
Conclusion :- We Reject H0

There is sufficient evidence to support the claim that standard deviation of the length is exceeds 1.2 cm.