A Lumber Mill Is Tested for Consistency by Measuring the Variance

A lumber mill is tested for consistency by measuring the variance of board thickness. The target accuracy is a variance of $0.0035$ square inches or less. If 28 measurements are made and their variance is $0.006$ square inches, is there enough evidence to reject the claim that the standard deviation is within the limit at $\alpha = 0.01$ ?

A) Yes, since the $\chi ^ { 2 }$ test value $8.91$ is less than the critical value 48.278.
B) Yes, since the $\chi ^ { 2 }$ test value $8.91$ is less than the critical value 46.963.
C) No, since the $\chi ^ { 2 }$ test value $46.29$ is less than the critical value $46.963$ .
D) No, since the $\chi ^ { 2 }$ test value $46.29$ is less than the critical value $48.278$ .

Correct Answer:

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