Quality Quiz from Professor Cleary
"B" is correct.
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Tabby the cat should be happy, since LaMal’s theory is dead wrong.
Control limits become wider because of the A2 value used to calculate them, and the R-bar changes, not because of variability within the sample.
Sample #8 has a sample size of 5. The calculation of control limits for that sample (and all other samples with a size of 5) follows. The proper A2 value when n = 5 is .577.
Sample #9 has a sample size of 2. The control limits are wider than those of Sample #8. The proper A2 value when n = 2 is 1.88.
It is also to be noted that the R-bar changes as the sample size changes.
It is easy to see in this example that when the sample size becomes smaller, the control limits become wider. A logical explanation is that with a smaller sample, the estimate of the mean is less likely to be accurate, so control limits must become wider. On the other hand, with a larger sample—say, 10—the control limits would be tighter because of more accurate prediction of the mean.
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