Respond to the discussion post below with YOUR educated opinion in 3-4 sentences WITH scholarly source backing it up
The formulas for z intervals and t intervals are similar but the distinction lies in the knowledge or lack thereof of a sample standard deviation. When the sample standard deviation is unknown because of lack of data about the sample population it is referred to as a T interval.
A T interval can be used to learn more about a mysterious sample population. Even without the known data the T interval still defines a range of values for the answer.
The confidence part is distinct from the interval but it is still an important component without which the data could not be analyzed. The confidence level is usually 90% or 95% and sometimes even 99% defining that the analyst is extremely confident in the results.
An analyst would most likely use a T interval equation to determine the potential of new instruments to be sold. At first I plan to start with amplified harmonicas but I would like to use this T interval to determine which instruments are most likely to become popular. This could be accomplished by pulling data on demographics in the areas I want to conduct business then using that data to work out values I can use in the T interval. When I’ve determined with a 90% probability a market that has a high probability of succeeding I’ll focus my efforts on that instrument first and then probably run the T interval again each time I plan on releasing a new instrument most likely about once a year.
A Z interval like a T interval shows the range of acceptable values. A good example of these acceptable values is seen in weather reports when the weather station reports possible highs and lows in the daily temperatures such as 76 to 95 or the level of the snowfall such as 3500 to 4500 feet. The only difference between T intervals and weather reports is that weather reports operate on a 50% confidence level or even lower in some cases given the massive number of parameters they have to account for: wind speed prevailing weather patterns offshore low-level systems onshore low-pressure systems and so on.
Something that occurs to me while thinking about this is that business owners have a lot of parameters to consider too such as market demand supply interest rates government regulatory activity and many more. As a question how do business analysts arrive at a stronger confidence level than weather analysts?