Suppose a local manufacturing company claims their production line has a variance of less than 9.0. A quality control engineer decides to test this claim by sampling 35 parts. She finds that the standard deviation of the sample is 2.12. Is this enough evidence at the 1% level of significance, to accept the manufacturing companies claim? Calculate the appropriate test statistic (round to 2 decimal places as needed)

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  

   The level of significance is

The null hypothesis is  

The alternative hypothesis is  

Gnerally the test statistics is mathematically represented as

=>

Generally the degree of freedom is mathematically represented as

=>    

=>    

From the chi - distribution table the  critical value of at a degree of freedom of   is  

From the value obtained we see that the test statistics does not lie within the region of rejection (1.e 56.060 ,   )

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

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