right 2.0 four five this is where my tails begin so the right tail begins at positive two point zero five four or five and the left tail begins at negative two point zero four five now this is really important that you have the number line in your head okay a lot of people mess this up or have trouble with it especially intro students when they don't get the number line in their head remember in between negative two and positive two would be zero zero sort of in the middle of a t-distribution and then if you keep going negative this will be like negative four way out here keep going positive gonna get positive four way out here so how those numbers in your head the tail begins at the critical value and the percentage in the tail is determined by the significance level in this case there was two tails now here's the big question does the test statistic positive two point five seven one fall in the tail remember what we said was the tail room right if the test statistic falls in the tail determined by the critical value then and and the significance level then the sample data significantly disagrees with the null hypothesis it's not just a little bit of a disagreement it's a significant disagreement okay so where is two point five seven one all right where is that well let's find out let's see here's two point five seven one where is that on the number line well two point five seven one would be bigger than two point zero four five right wouldn't it be sort of in here here's where my test statistic is falling there's my my t-test statistic right my test statistic is falling in the tail so what does that tell us well it tells us that our sample data or sample statistics significantly disagrees with the null hypothesis so if this was a one population mean test for example it would tell me that the sample mean significantly disagrees with that population mean the null hypothesis okay so think in the tail means the sample data significantly disagrees with the null hypothesis remember the sample data always disagrees with the null hypothesis this is not talk asking if the sample data stick just disagrees this is it doesn't significantly disagree if the test statistic could fallen over here then it's probably it just disagrees a little bit and it's not really a significant disagreement that's probably just due to sampling variability okay so what this is telling us when it falls in the tail that it's a significant disagreement all right let's look at another one so now we got example - we got a left tailed test with a z-score so this is probably some kind of proportion test or a percentage test so we're looking at a z-score test statistic of negative one point seven one seven three negative one point one seven three we're doing a significance level of 0.01 or alpha equals point zero one or one percent again I can look those numbers up on look up the critical value on stack key under theoretical distributions normal just like we did in the last unit when we looked up critical values by the way you can look up critical values with charts some stat classes still do that I'm not a big chart guy I really like to use technology I prefer to use that key to look up the critical values if I need one a lot of computer programs that will just give this to you right at the start so yeah once you get your printout for your hypothesis test you'll see that this is given to you so what I did was I I went to the normal theoretical calculator in stat key and I just clicked left tail and then I put in the percentage in the left tail as point zero one that's a significance level and then the computer calculated how many what would be the critical value over where with the tail start with you're dealing with a z-score test statistic so this is sort of the number of standard errors that needed to be so the computer thinks that the test statistic has to be lower than negative two point three to seven to be considered significant okay so again think of member the number line right negative two point three negative four is out here zeros in the middle here's one okay so here's our test statistic negative one point one seven three where does that fall compared to the tail well negative one point one seven three right where does that fall where does that fall well it's gonna be kind of over here right my test statistic is around negative one so my test statistic my test statistic is falling over here it's not in the tail it's not in the tail determined by the critical value okay so not in the tail this means that the sample data only disagrees with the null hypothesis a little bit it does not significantly disagree okay it's only a little bit of a disagreement and probably that disagreement might just be due to sampling variability okay so again not in the tail tells me that the sample data does not significantly disagree with the null hypothesis if this was a one tailed I was sorry one population proportion test this would tell me that the sample proportion is actually pretty close to the population proportion and the null hypothesis in fact it's only one point one seven three standard errors away if you're dealing with a two population proportion test it would be dealing with the sample proportion for Group one is only one point one seven three standard errors below group two but again that's not very much again the computer thing to thought it had to be at least negative two point three to seven or lower to be considered significant so this is not significant my sample statistic does not significantly disagree with the null hypothesis or you can think of it as your sample data does not significantly disagree with the null hypothesis okay so in another one here's example three now we had a right tailed test with a chi-square test is no net even if you don't understand everything about the test statistic again you still can get the idea of what this tells you about the data chi-square again is a more advanced kind of test statistic in fact it's not a normal in fact it's a non normal distribution we kind of talked a little bit about chi-square in our last unit but basically if I was lead over the degrees of freedom for the chi-square distribution looks kind of very skewed right but it is it's the kind of same idea they said that they're using a significance level of 10% point 100 on and it's a right-tailed test so the right tail the probability in the right tail is going to be point one of again I'll go to the chi-square theoretical distribution calculator and stat key and I put in degrees of freedom for and right tail and then change the percentage to point one zero and there's my critical value all right that's where my tail starts so chi-square is a lot different than T's or Z's T's and z-scores usually get significant around to Chi square it's usually you're quite a bit bigger before they get significant because they're squared numbers added up so this one tells me the critical value came out to be seven point seven seven nine again I looked that up on stat key so think of it this way again always draw yourself a picture like I did here draw yourself a picture the day of the right tail shade the right tail put the print significance level percentage in the right tail and then the tail starts at this seven point seven seven nine so think of this is a chi-square value that you can compare your test statistic to okay so my test statistic came out to eleven point three to eight so where is that again okay in chi-squared zeros over here and three and here's seven point seven my critical value and here's 12 well where's 11 eleven point three it's kind of over here right it's pretty close over here there's my there's my test statistic so my test statistic is definitely in the tail right in the tail this 11.3 is over here in the red in the tail it's not over here if it was just over here it would not be significant it would just probably be due to sampling variability over here again very significant so again this is again telling me that the sample data significantly disagrees with the null hypothesis because it fell in the tail all right so we want to kind of get you this this rule about tails how do I read my tails that's kind of the key idea when you're dealing with test statistics alright in our next video where I'll talk a little show you again how I calculated these critical values on stat key and talked a little bit about using technology all right so this has been intro to hypothesis testing test statistics I'm about to show and this is intro stats I will see you next time