95% Intervals

#1
I'm new here (and relatively new to statistics) so I apologize if this thread is in the wrong place.

I have a problem that seems relatively easy but it has me stumped...

I need help with intervals on data. I thought tolerance intervals would work but they are not giving me what I want. I have a population of values-the entire population, and I have the mean, and standard deviation and I think the values are normally distributed. I know that every value falls between two numbers that I have set (for my first interval every number falls between 0 and 4.99 for example). I need to know the two values between which 95% of the population falls, as well as the upper number below which at least 95% of the population falls, and how to do this calculation and what it is called. When I try other types of interval calculations (ie tolerance) the upper value ends up being above 5 and the lower value below 0, which I know are not correct because NO value in my set falls above 4.99 or below 0. If anyone could give me any help or at least tell me what this type of calculation is called I would be incredibly grateful.

Thanks...
 

Mean Joe

TS Contributor
#2
When I try other types of interval calculations (ie tolerance) the upper value ends up being above 5 and the lower value below 0, which I know are not correct because NO value in my set falls above 4.99 or below 0. If anyone could give me any help or at least tell me what this type of calculation is called I would be incredibly grateful.
1) The name for the type of interval is confidence interval. There is the two-sided confidence interval (abbreviated CI) for getting "the two values between...", and the one-sided CI for getting "the upper number below...".

2) Sometimes the calculation gives you a number that is outside of your defined range. eg lower limit = -1. In such a case, you just amend the calculated interval to not go outside your range.
 

Dason

Ambassador to the humans
#3
I need to know the two values between which 95% of the population falls, as well as the upper number below which at least 95% of the population falls, and how to do this calculation and what it is called.
1) The name for the type of interval is confidence interval. There is the two-sided confidence interval (abbreviated CI) for getting "the two values between...", and the one-sided CI for getting "the upper number below...".
I don't think a confidence interval is what they're looking for. A tolerance interval sounds like what they want. The problem seems to be that they're (most likely) using some sort of normal theory when their data probably isn't normally distributed.

Do you know for sure that the min/max is 0/4.99 or is that estimated from the data? One thing that might work is to create a scaled/shifted Beta distribution to have the max be 4.99. I don't know if there is any research into tolerance intervals for the beta distribution though.
 
#4
Joe and Dason - Thank you guys for the help. I know for sure that the min/max is 0/4.99, it's not estimated from the data. I assumed that the data was normal by doing a 'back of the envelope' test - taking the max/min values in my data set and calculating their z-score and comparing it to values in a standard normal data set. I admit though I may have done this incorrectly, or poorly...
 

Dason

Ambassador to the humans
#5
Did you plot the data? Did it look normal? Even then it would make more sense to use a truncated normal distribution. What is your sample size?