Answer :
Answer:
The decision rule is
Fail to reject the null hypothesis
The conclusion is
There is no sufficient evidence to accept the manufacturing company claims
Step-by-step explanation:
From the question we are told that
The sample size is n = 35
The sample standard deviation is [tex]s = 2.12[/tex]
The level of significance is [tex]\alpha = 0.01[/tex]
The null hypothesis is [tex]H_o : \sigma ^2 = 9.0[/tex]
The alternative hypothesis is [tex]H_a : \sigma ^2 < 9.0[/tex]
Gnerally the test statistics is mathematically represented as
[tex]X^2 _{stat} = \frac{(n -1) * s^2 }{\sigma^2 }[/tex]
[tex]X^2 _{stat} = \frac{(35 -1) * 2.12^2 }{9 }[/tex]
=> [tex]X^2 _{stat} = 16.98[/tex]
Generally the degree of freedom is mathematically represented as
[tex]df = n - 1[/tex]
=> [tex]df = 35 - 1[/tex]
=> [tex]df = 34[/tex]
From the chi - distribution table the critical value of [tex]\alpha[/tex] at a degree of freedom of [tex]df = 34[/tex] is
[tex]X^2_{\alpha, 34 } =56.060[/tex]
From the value obtained we see that the test statistics does not lie within the region of rejection (1.e 56.060 , [tex]\infty [/tex] )
Then
The decision rule is
Fail to reject the null hypothesis
The conclusion is
There is no sufficient evidence to accept the manufacturing company claims