### Video instructions and help with filling out and completing How Form 2220 Calculator

**Instructions and Help about How Form 2220 Calculator**

In this tutorial I'm going to talk about the T distribution and the T distribution is very similar to the z-score I'm going to review a little bit of that as well but first I want to tell you a little bit about the history of the T distribution normally I don't talk about things but this is William Gossett and what makes him interesting interesting is is he actually used the T distribution to help improve Guinness beer where he worked so he helped make tasty beer now the normal distribution looks like this and in the green area we have the acceptance area and in the red area we have the rejection regions and this is called a two-tailed test 95% of the area of the curve is in the green area and 5% are in the rejection area or 2.5% in each tail sometimes the tails are referred to as alpha and if you're in a fraternity or sorority you probably know that already and that's equal to point zero to five and sometimes it's called a p-value which is also known as the probability value right there or the p-value so now we have the Z scores and the Z scores are 1.96 and negative 1.96 remember that's the number of standard deviations away from the mean 1.96 is just about to and that's important because I tell my students you know when you get to 2 is a lot easier to remember than 1.96 and this 2 value is going to be important for T statistics as well or the T distribution also we write it like this so we say if Z is less than or equal to negative 1.96 or if Z is greater than 1.96 we reject the null hypothesis or if Z is about 2 or negative 2 now the T distribution or T test looks about like this little gold or the curve right there and it's shaped it's a little shorter let me bring in the normal distribution so you can kind of compare and it's shorter and fatter than the normal distribution it's probably self-conscious about that as well so let me fade out the normal distribution and so the curve again looks very similar to the bell curve we do the same thing we put 95% the middle and then we put in the rejection regions we put 2.5% in each region now imagine that this sample size is equal to 2 which is very small we would set up a critical region or T score would be negative 12 point 7 and 12 point 7 so we say if T if T is less than or equal to negative 12 point 7 or if T is greater than or equal to 12 point 7 we reject and what to do reject reject the null hypothesis so we reject if it's greater than 12 point 7 or less than negative 12 point 7 I'll put the normal distribution back in and that's what that is and now that's the T distribution what happens is if the sample size goes up as the sample size goes up the T distribution becomes more and more like the normal distribution until eventually here we go it is exactly the same as the normal distribution especially at large samples actually only large samples so at large samples really samples greater than 20 you're going to get the same result you'll find this table at the back of most stats books and this is for a two-tailed test where we have 5% of point zero five in the two tails two point five percent in the tails and of course there are two tails that add up to five percent that little DF up in the left-hand corner there that yellow now stands for degrees of freedom and degrees of freedom are simply sample size minus one is equal to degrees of freedom if we have a sample size of two our degrees of freedom is one and that's where we get the twelve point seven zero six or twelve point seven that I used before from this table now as the sample size gets larger so does the degrees of freedom and if you notice that 19 degrees of freedom the sample size is 20 which is equal to and the critical area is equal to two point zero nine three which is highlighted by the red there which is very close to 1.96 or about two not very large samples infinity or anything larger than 100 the critical value is 1.96 and it's exactly the same as the normal distribution or theoretically the same I should say degrees of freedom is equal to sample size minus 1 sample size greater than 20 T is similar to Z very similar to Z and that's it for this tutorial.