okay um so let me just also really quickly say that um we've done these sorts of problems it seems like there are no other questions you can all you can now you should be able to now also do these sorts of problems when you have to use the T distribution as you might expect it all works exactly the same except instead of Sigma you're using s and instead of Z you're using and everything else you already know okay I'm just going to throw in one exception to that and this is something that I didn't mention before uh I gotta find a problem for this okay so find the 95 content from you if you have from our sample X bars 124 s is 8.6 n is 81. so the first thing we should so first thing I always do is just write down the formula because then I know what I'm doing so the confidence interval is going to be X bar plus or minus what t times s of X bar that was easy to figure out okay so do we have X bar yes it's 124. do we have t no not yet and do we have S for X bar no yeah we don't have it but it's pretty easy to find s for X bar equals square root of so it's 8.6 over the square root of 81. let's work that out equals 8.6 divided by the square root of 81 which is 9 by the way uh uh 0.9556 um you should I mean you should do the check uh so normal no use t-score or t distribution whatever okay um in particular it's a good habit uh because you should you should always make sure that you're checking instead of just using the normal distribution out of habit um so I like to say it's a step make sure okay so to go back SRX bar we know that's easy it was 0.9556 so now we need to find T what's going to help us find T roll so what do we draw 0.95 in the middle so now what oh now we're trying to find the t-score okay so first I'm going to use stat disk uh because that's by far the easier one analysis distribution oops we want T distribution so what do we need to fill in degrees of freedom which was 80 and what's the area to the right 0.025 there you go the T value is 1.99 yeah and then of course also negative 1.99 but a formula takes care of that now how do we do this using Excel t-n of probability degrees of freedom so probability okay so the question is what probability do we put in it should be negative one the probability for T ends for some reason Excel wants both tails o5 degrees of freedom was 80 and there you go up to rounding there it is right right so let's go back and fill that in the formula so this is 1.99 and now we can continue to work this out 124 plus or minus we have to figure out what this is tons uh point six six sorry nine five five six that gives you 1.9016 okay and if we work out the upper and lower bounds we get six what happened oh 124 Plus 1.99 so we get 122.0984 and 125 9016. so I can say uh okay so the 95 confidential from you is that uh you don't mean for completeness you can but yeah you can you can leave it to the to the account to the formula it's okay so if you were to finish filling it in on the picture uh 124 is here 2.0984 and 125.9016 . okay so again with the T distribution works out basically the same so any questions on these things okay