How to calculate confidence interval not on t-table

[Notoriousb3]

So as the title says. How do you calculate the confidence interval that is not on the t-table. For example how do you calculate the confidence interval for 97%? Assume that it is a normal distribution, you are not given σ and that n<30. Is there a formula? Or should i look for a more specific t-table?:P

 

[I like Serena]

So as the title says. How do you calculate the confidence interval that is not on the t-table. For example how do you calculate the confidence interval for 97%? Assume that it is a normal distribution, you are not given σ and that n<30. Is there a formula? Or should i look for a more specific t-table?:P

You need a calculator that can calculate the inverse of the cumulative t-distribution.

In Mathematica this would be: inversecdf[ studenttdistribution[n-1], 0.015 ] for the lower bound, which is negative.
In this formula n-1 is the so called "degrees of freedom", usually designated "df".
And 0.015 is half of the remaining chance, which is (1 - 0.97) / 2.
Since the t-distribution is symmetric, the upper bound equals minus the lower bound.

You can evaluate this for yourself on the web:
http://www.wolframalpha.com/input/?i=inversecdf[+studenttdistribution[29

Does this answer your question?

 

[Notoriousb3]

Sorry but I don't understand your response what is "inversecdf" and "studenttdistribution". Also what kind of calculator would I need to calculate the inverse of the cumulative t-distribution? I'm rolling on a ti-83 plus and this baby has yet to fail me. Just to be clear, I know how to calculate a confidence interval for the following 80%, 90%, 95%, 98% and 99%. But I would like to know how you would calculate the confidence interval that cannot be solved with the student t distribution. i.e 93%, 97% etc.

 

[I like Serena]

Sorry but I don't understand your response what is "inversecdf" and "studenttdistribution". Also what kind of calculator would I need to calculate the inverse of the cumulative t-distribution? I'm rolling on a ti-83 plus and this baby has yet to fail me. Just to be clear, I know how to calculate a confidence interval for the following 80%, 90%, 95%, 98% and 99%. But I would like to know how you would calculate the confidence interval that cannot be solved with the student t distribution. i.e 93%, 97% etc.

The offical name of the t-table is the student-t-distribution-table.
"inversecdf" stands for the inverse of the cumulative distribution function.

To calculate this on a graphical calculator you can use the invT-function.
However it seems this function is not available on the ti-83+, but is available on the ti-84.
But there are ways described on the internet how to do this anyway with the ti-83+.

I found a youtube video describing exactly you problem and how to solve it on your calculator:



And I found another procedure to calculate invT on:

http://www.angelfire.com/pro/fkizer/Instructions/tiusrmanstat83.htm"