Period 1 (observations 1-25) before a training program was instituted; Period 2 (observations 26-50) after the training was completed. First, we verify that the data are from a population that is Poisson distributed using a Poisson distribution test for both periods, and the p-values show that this is the case (p-value period 1 = 0.1596; p-value period 2 = 0.9557). Moreover, the tests already show an improvement in the mean error rate (decrease in lambda from 16.32 to 7.92)

    Poisson Distribution Fit Test Using Variance and Mean

data:  input data
chi.square = 34.279, degrees of freedom = 24, p-value = 0.1596
alternative hypothesis: true chi.square is not equal to 24
sample estimates:
     chi.square sample variance     sample mean 
       34.27941        23.31000        16.32000 

    Poisson Distribution Fit Test Using Variance and Mean

data:  input data
chi.square = 23.717, degrees of freedom = 24, p-value = 0.9557
alternative hypothesis: true chi.square is not equal to 24
sample estimates:
     chi.square sample variance     sample mean 
      23.717172        7.826667        7.920000 

With the help of control charts for attribute data (in this case, a c chart), we can visually assess if the process is in a state of control before and after the training. If yes, we can also assess if the training implemented resulted in any improvement in performance regarding the error rates. As the statistical test already confirmed, it is also visually evident that the mean error rate decreased significantly from period 1 to period 2 thanks to the training program.