Final answer:
A confidence interval around the mean monthly police complaints can determine if they are 'in control' at a 90% confidence level. To do this, calculations are essential to see if complaints fall within the expected range, indicating a stable pattern over the year.
Step-by-step explanation:
The concept of using a confidence interval is central to inferential statistics, and it is used to gauge the reliability of an estimate. A confidence interval can be constructed around a sample mean to give an estimate of the range in which the true population mean is likely to lie. A 90% confidence level indicates that if we were to take many samples and build a confidence interval from each of them, about 90% of these intervals would contain the true mean of the population.
For the police chief's annual review using the monthly complaints, they would need to calculate the mean and standard deviation of the complaints and then use these to construct a confidence interval. If the number of complaints in subsequent months falls within this interval, we can say that they are 'in control' or within an expected range.
An hypothesis test could be employed to formally decide if the complaints are consistent or if there's a significant variation from month to month. However, simply by observing the variability in the data provided, a professional statistician would still need to calculate the confidence interval to conclusively determine whether the number of complaints is in control or not.