Discussion Response
Respond to the discussion post below with YOUR educated opinion in 3-4 sentences WITH scholarly source backing it up
Z and T confidence intervals are different based on the sample size and whether or not the standard deviation is known. Generally, if a sample size (n) is greater than 30 and the standard deviation is known, than a z confidence interval or z score is used. On the other hand, if n<30 and the standard deviation is not known, then a t confidence interval or t test is used. These differences in t and z are results of the fluctuation in the t test sample variances.
A z test, or z confidence interval could be used at a donut shop that produces donuts in house. The owner of the shop could use a z score to determine the probability that a donut will fall between the acceptable size limits, or standard deviations, of donut sizes. If they sample donuts (50 out of a daily batch of 500) and have a determined standard deviation, they can with confidence predict the probability that a donut will fall in or out of the acceptable size limits.