The mean of the sample means and the pooled standard deviation of 36 samples of size 9 taken from a production process under control are ,and S = 6,respectively.The lower control limit of the 3-sigma chart is 147.

Question

The mean of the sample means and the pooled standard deviation of 36 samples of size 9 taken from a production process under control are  ,and S = 6,respectively.The lower control limit of the 3-sigma  chart is 147.

Quizplus · Accepted Answer

The lower control limit of the 3-sigma chart is calculated as:
LCL = mean - 3*S/sqrt(n)
where n is the sample size. 
Substituting the given values, we get:
147 = 11ea78b9_2e5e_d113_8379_93afff7fef43_TB4388_11 - 3*6/sqrt(9)
147 = 11ea78b9_2e5e_d113_8379_93afff7fef43_TB4388_11 - 18
11ea78b9_2e5e_d113_8379_93afff7fef43_TB4388_11 = 165
This is not the same as the given mean of sample means, hence the statement is false.

The Mean of the Sample Means and the Pooled Standard