Statistics Problem: Sampling Distributions - Somewhat OT

[AtlBraves]

You are on the staff at the Post Office. Your job is to find a process to find the average waiting time for service. How do you collect the data, and once it is collected, what do you do next?

 

[doxigywlz]

what? Average waiting time would equal the amount of time a customer waited. You'd have to pick a certain amount to be constant-- such as how many customers' wait time you are counting. By collecting the data, how would you find out their wait time? i.e., they take a ticket when they get there with the time stamped on it, and when there number s called, wait time end. after that, you add it all up and divide by the number of customers who's wait time was included.

 

[tacman]

As a statistician on the staff at the Post Office, my first step would be to define the population of interest. In this case, it would be all customers who come to the Post Office for service. Next, I would determine the appropriate sample size that would accurately represent the population. This would involve considering factors such as the size of the Post Office, the frequency of customers, and the resources available for data collection.

To collect the data, I would use a systematic random sampling method. This involves selecting a random starting point and then selecting every nth customer in line for data collection. This method ensures that every customer has an equal chance of being selected for the sample.

Once the data is collected, I would calculate the average waiting time for service by dividing the total waiting time for all customers by the number of customers in the sample. This would give me an estimate of the average waiting time for service for the entire population.

To ensure the accuracy and reliability of the data, I would also calculate the margin of error and confidence interval for the average waiting time. This would give us a range of values within which the true average waiting time is likely to fall.

Additionally, I would use statistical software to create a sampling distribution of the average waiting time. This would allow me to visualize the distribution of the data and identify any outliers or patterns.

Based on the results, I would make recommendations for improving the waiting time for service at the Post Office. This could involve implementing new processes or increasing resources to reduce the average waiting time.

In summary, as a statistician at the Post Office, I would use systematic random sampling, calculate the average waiting time and its confidence interval, and use statistical software to analyze the data and make recommendations for improving service. This process would help us accurately estimate the average waiting time for service and make informed decisions to improve customer experience at the Post Office.