Using t-statistic - HW question

[Matt M]

Hello,

I've been staring at this question for days and I blame this book for doing a horrible job teaching it because I cannot make any sense of the question after going through the chapter. Anyway, here is the question:

Consider a sample X1,....,X2 of normally distributed random variables with mean u. Suppose that n = 16.
What is the value of c for which P(|4(X-)/S| <= c) = 0.95

I also know the answer is to solve for P( <= c) = 0.95 gives c = = 2.131

What is the work in between??

Thank you!

Matt.

[Dason]

Hey Matt. First it seems like you know how you want your math to be formatted but don't know how to do it on the forums so I would suggest checking out this thread.

I think what you're asking was how to get from your first probability statement to the second one in a rigorous way. I guess my question for you is what definitions you know for a t-statistic? Do you have something in terms of the ratio of a normal r.v. and and a chi-square r.v.? Or does you book use something else?

[Matt M]

Thank you Dason for you suggestion I applied those changes.

I knew nothing about chi-square that you mentioned so upon looking into it in the book it lead me to the t-distribution which explains where came from and I deduced the rest. Thanks for you help!

Matt.