# 7Sample Size

## 7.1 Mean

To have confidence in the conclusion of any statistical analysis, we must ensure that the number of samples (*n*) is sufficiently large. As an example, consider the batch blending quality data in Table A1.7. By calculation, the 78 results have a mean of 97.9 and a standard deviation of 9.1. To have confidence in our estimate of benefits from improved control, we need the confidence interval of the estimate of the mean. We showed in Section 4.7 that estimates of the sample mean, calculated using different selection of *n* results from the population, will have a variance of . Choosing a confidence interval from Table A1.8, for example 95%, gives a value of 1.96 for *z*. The margin of error (*ε*) is therefore

In other words we are 95% confident that the population mean lies between 95.9 and 99.9. If we wanted to improve on this we can determine the required sample size by rearranging Equation (7.1).

So, for example, if we wanted to improve the accuracy of the estimate of mean to ±1.0, we would need 318 results.

It becomes more complex if we want to check the confidence that the mean has changed, for example, as a result of implementing control improvements. ...

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