Enumerative versus Analytic Statistical Methods

How would you respond to the following question?

A sample of 100 bottles taken from a filling process has an average of 11.95 ounces and a standard deviation of 0.1 ounce. The specifications are 11.9 12.1 ounces. Based on these results, should you

1. Do nothing?

2. Adjust the average to precisely 12 ounces?

3. Compute a confidence interval about the mean and adjust the process if the nominal fill level is not within the confidence interval?

4. None of the above?

The correct answer is d, none of the above. The other choices all make the mistake of applying enumerative statistical concepts to an analytic statistical situation. In short, the questions themselves are wrong! For example, based on the data, there is no way to determine if doing nothing is appropriate. Doing something implies that there is a known cause and effect mechanism which can be employed to reach a known objective. There is nothing to suggest that this situation exists. Thus, we can t simply adjust the process average to the nominal value of 12 ounces, even though the process appears to be 5 standard errors below this value. This might have happened because the first 50 were 10 standard errors below the nominal and the last 50 were exactly equal to the nominal (or any of a nearly infinite number of other possible scenarios). The confidence interval calculation fails for the same reason. Figure 8.1 illustrates some processes that could produce the statistics provided above.

Figure 8.1. Possible processes with similar means and sigmas.

The following analytic statistics questions might be appropriate: