Hi there - thanks for your query - although our forums are not open until next month, we thought it might be helpful to provide you a response.
Please let us know if you require more information. We’d also love to hear other people’s thoughts.
The Company have seen that one of the observers got 30 out of 42 of their guesses correct (which is 71.4%). This is lower than the 86% (or 36.12 out of 42) accuracy rate that they have worked out for all observers in general.
The key here is that it is every observer will have a different accuracy rate as each person is different and each situation is different and this is what sampling variability is all about.
86% is the expected or average accuracy rate. It would be good to run a simulation with an accuracy rate of 0.86 (this can be used as the probability that they will guess the right age range for each group of 42 shoppers) to see the range of possible accuracy rates that could happen due to sampling variability.
Think of the results in a dot plot: you would expect to see the accuracy rates generated in the simulation to be mostly grouped around the expected rate of 0.86 with fewer dots the further away you get from this expected value.
After running the simulation to see this range of generated accuracy rates, the company can see if this observer’s rate is likely or not. If it is not a likely accuracy rate, then this suggests that the observer probably does have a lower than expected accuracy rate.