okay here we go all right so next what if we don't know the population standard deviation Sigma so remember the first thing I said is well we've been saying we know mu it doesn't make sense to say that we know mu well what is sick because we don't know anything about the population well what is Sigma Sigma is a standard deviation of the population so if you think about it it doesn't make a lot of sense to say that we know that either so we're now going to extend uh further into reality the sort of problem that we can handle um so there's mostly good news a little bit of bad news so here's the good news if we don't use Sigma which is the standard deviation of the population what can we use instead yes the standard deviation of the sample now you all remember the notation for that standard deviation s okay so that's the good news here's the bad news there's a price to pay for using S is no longer normal so what's the distribution how do we find probabilities oh Maya coming in strong she knows this edition of X bar in this case is What's called the student T distribution we just call it the T distribution thank you here's the good news it's similar to the normal distribution it's symmetric the middle value is zero and quite honestly when you draw the picture of it it looks almost the same as the normal distribution all right here's the bad news the distribution changes depending on N which is how big your sample is the one thing that you also have to put in is What's called the degrees of freedom which I'm going to abbreviate DF here's the good news it's just n minus 1. okay so let's so let's figure some things out uh I'm gonna skip just fit okay so first I'm going to show you how to do the T distribution using Excel then I'll show you using stat disk so let's say we have a value of 0.5 well what's the what's the what's the command for what's the command if we have the normal distribution it's Norm dist to normal s disk so what's the command for T distribution no Norm T Test I don't know okay now when you put in key dist what do you have to tell it right you have to put in the X you have to put in your degrees of freedom and you have to put in tails in this case Excel is nice to give you the option of saying how many tails you want so let's say that our T value is 0.5 our degrees of freedom is 29 let's say I want the area in one tail there you go here's what you have to put in now this is also a little bit of a misnomer it says X it really should say t you have to put in a t value X degrees of freedom and Tails it says X it really should say t putting your T value there sorry yeah that's what Excel does um as far as drawing the picture goes honestly the t-distribution pretty much looks like the norm distribution so the picture looks pretty much the same a little different but not much okay so now let me show you how to do this using stat disk go to analysis distribution now which distribution do we want student T distribution so notice that you have to put in the degrees of freedom don't forget to change it then the T value well the one we were just working with was 0.5 and then you click evaluate there you go it tells you again area to the left area to the right two tails and Central so it tells you all the things that we now realize we might need foreign yes oh for Excel okay so back to excel T disc parentheses and then it prompts you for an x value which is really a t value degrees of freedom and how and how many tails so what are the options for how many tails one or two exactly exactly okay