How do you answer this?
Response 1:
There are two big difference between z and t confidence intervals. One main difference between the confidence intervals z and t is that the population standard deviation is known with the z confidence interval and it is unknown for the t confidence interval. The other difference is that t is usually used when the sample size is small, and z is used when there is a larger sample size. One such use of a z confidence interval would be to look at the efficiency and speed of a conveyor system within a warehouse operation.
I work in a warehouse where speed of our conveyor system is a point of focus and pride for the company. Analysts are consistently looking at data to see the average time it takes for material that an order-picker fills an order to be sent down the conveyor and when it is fully packaged and put on a shipping vehicle. This data can be assessed by the use of a confidence interval. Due to system stoppages and other disruptions, no two trips from picking an item to its shipment run the same length of time, so a confidence interval would be a useful tool to test samples of these ship times to see how the operation is running overall. By looking at the interval around the mean, management can decide if operations need to be made more efficient. The z interval would be used in this case because there would be thousands of samples per day to use, thus making the use of t interval inefficient due to the large sample size.
Response 2:
Before I dive into the difference between the two, let’s first talk about what a confidence interval is exactly. A confidence interval is when you use a sample as an overall unknown population value. For example, when you see polls talking about a certain percentage of Americans prefer one product over another. It’s not like someone actually called every person in America and asked them, they took a small sample that would represent the area as a whole. Now on to what the differences are. There is one major difference between the two and that is that Z- intervals we assume that the population standard deviation is known and with the T- intervals we know it is not. The T-interval relies on the actual small sample size. Z-interval is better to use when your sample size rather large and the T-interval is better for smaller sample sizes. Now on to my example.
As I have said many many times, I work for a college bookstore. I am the web manager so it is my job to make sure that all online orders are filled and packaged properly and in a timely manner. On a daily basis we have to package online orders to be picked up in our store by students. This can be a tricky task to be done efficiently because most people don’t want to take the time to do it properly and just want to go home. This is where confidence interval comes into play. We have numerous employees who package our orders so not one person is doing it in the same time frame. We can use the confidence interval to measure the efficiency that this is being done and the timeliness that a student gets their order. This will help us know if we need to improve on our overall packaging time or if we are where we need to be. Depending on the time of year, we would potentially use both a z-interval and a t-interval. We would use the z-interval during our busy time known as rush (beginning of semesters) and a t-interval would be used during our slower times (middle of semesters).
References:
Math Boot Camps. (2017) Confidence Intervals for the Mean- By Hand. MathBootCamps.com. Retrieved from https://www.mathbootcamps.com/calculating-confiden…
