A lumber mill is tested for consistency by measuring the variance of board thicknesses.The target accuracy a variance of 0.0015 or less.If 22 measurements are taken and their variance is 0.006, is there
Enough evidence to reject the claim that her standard deviation is within the limit at ?
A)Yes, comparing the test value 84.00 and the critical value 38.93.
B)No, comparing the test value 18.33 and the critical value 38.93.
C)Yes, comparing the test value 84.00 and the critical value 40.29.

Question

A lumber mill is tested for consistency by measuring the variance of board thicknesses.The target accuracy a variance of 0.0015 or less.If 22 measurements are taken and their variance is 0.006, is there
Enough evidence to reject the claim that her standard deviation is within the limit at  ?
A)Yes, comparing the test value 84.00 and the critical value 38.93. 
B)No, comparing the test value 18.33 and the critical value 38.93. 
C)Yes, comparing the test value 84.00 and the critical value 40.29.

Quizplus · Accepted Answer

We can use the F-test to determine if there is enough evidence to reject the claim that the variance is within the limit.

The test statistic is:

F = sample variance / target variance

F = 0.006 / 0.0015

F = 4

The critical value for F with 21 and 1 degrees of freedom (since there are 22 measurements) at a 0.05 significance level is 38.93.

Since our calculated F-value of 4 is less than the critical value of 38.93, we fail to reject the null hypothesis that the variance is within the limits. Therefore, there is not enough evidence to reject the claim that the standard deviation is within the limit at 11ebb61d_fc05_13ad_92a9_9f25ad7d6dd2_TB8376_11.

A Lumber Mill Is Tested for Consistency by Measuring the Variance