hi everyone this is Matt to show with intro stats today we're continuing our discussion about the basics of hypothesis testing we've kind of been going through the hypothesis test a little bit we talked about null and alternative hypothesis test statistics we talked about the idea of p-value so now we're kind of getting to this point where we're going to start to see if we can write a conclusion a final conclusion for the hypothesis test so today is all about writing conclusions so let's get started all right so um the one thing about a conclusion is saying that you reject the null hypothesis or fail to reject the null hypothesis is not actually a conclusion a conclusion has to address the claim it has to address what the person in the article said or what the person asks you to figure out and you have to talk about whether or not you have some evidence towards what you're saying so it's all about claim and evidence so it's really a statement about claim and evidence now to kind of get the idea of what's possible in a conclusion let's kind of go back a little bit to what we learned about p-value so in our last videos we've been kind of going through p-value and we found that if the p-value was less than or equal to the significance level right that means it's unlikely to be sampling variability it means that we had also means that we have evidence right that low p-value is considered evidence if it came from unbiased sample data so so again what we said was that the p-value was less than or equal to the significance level it's unlikely to be sampling variability that means we're allowed to reject the null hypothesis okay reject the hypothesis and that low p-value from unbiased sample data would be considered some evidence towards that so rejecting the null hypothesis but again well that's great if the if the null hypothesis was the claim we would just say that we gonna reject the claim but what if the claim was actually a che what if the claim was the alternative the opposite well then what you're allowed to do now is since you're saying you your evidence that the null is probably wrong so that's kind of giving us evidence that a che might be correct right or supporting a che so a low p-value tells you again that you're rejecting the null hypothesis and you're sort of supporting the alternative the alternative might be correct and we think the null is probably wrong okay now the high p value right we're talking about this in our previous videos about the high p value right so if a p value is more than the significance level more than our alpha or significance level then we're going to what we say fail to reject the null hypothesis right so we kind of talked about this how when you have a high pvalue you have a little bit of issue now that because it could just be sampling variability in other words the null might be correct and maybe your sample data disagrees just because of sampling variability or maybe the null is wrong it's really it's almost like you can't tell anymore if the null is right or wrong so the high p-value says tells us that we basically will fail to reject the null hypothesis that means you do not have evidence to reject the null hypothesis okay that's the way you want to think about it you don't have evidence to reject it now that doesn't prove that it's good that the null hypothesis is correct though it does lean in that direction the high p value kind of leans in the know might be but there's really no evidence for that well you have to be able to reject the null hypothesis to be able to support the alternative hypothesis so if you don't know if the null hypothesis is wrong you also don't really know that the alternative is correct or not so again what we would say for a high p-value would be that there's not evidence really to support the alternative hypothesis sort of makes sense so so again a high V value we're going to fail to reject the null it's like not evidence to reject the null hypothesis that's also not evidence to support the alternative hypothesis so what you see here is you really have sort of four options when you write a conclusion so it's either a high or a low p-value and then your claim what the person actually said in the article could be the null or the alternative so you have to kind of take that into account now I will say most of the time claims are usually the alternative hypothesis so you'll use support more often than you will reject but let's take a look at it so I got this little chart here that kind of summarizes it I hope it's helpful for you so if you notice so sort of we have maybe what did the person say is called the claim right the population claim one of the persons say or think is true about the population so if the claim was the null hypothesis that means that claim had some kind of equal to or not related or no effect in the null hypothesis and then your clip but also the claim might be the alternative maybe the person said something a statement that does not have an equal to part or involves change or effect or relationship so the claim that what the person said could be either one of these and you have to sort of take that into account when you write your conclusion now we also have the p-value right we could have a p-value that's lower than the significance level a low p-value and we could have a p-value that's high higher than the significance level now if the data came was unbiased and you know met all the assumptions for the test then a low p-value from some unbiased sample data would be considered some evidence and you have some evidence for what you're saying if it's a higher value then usually that's considered again not evidence you do not have significant evidence it could just be sampling variability now remember all of this works on how how unbiased is your sample how that's why we spent a lot of time in the class talking about biases but if your data a sort of representative of the population then a low p-value would be considered evidence now think about it this way what happens if I have some bad data what if I'm using some bad sample data that does not meet the assumptions well then this kind of goes up this era this kind of doesn't work anymore a low p-value from bad data is would not be considered evidence anymore because again that lis p-values based on data that does not represent the population so all of this works on how well your data is how how good is your data all right so let's assume that we got some really good data that mest met all the assumptions what would could we say well if the claim was that if they we had a low p-value then we would be rejecting the null hypothesis right but the null hypothesis is that if the if the null hypothesis was the claim that wouldn't be be rejecting the claim right that's exactly right we would be rejecting the claim right so I would say something like this there is significant evidence to reject the claim in other words I think the claim is wrong and I have some evidence to back that up now what happens if we have a high pvalue well remember a high p-value means it could be sampling variability and it's not considered evidence and so and we fail to reject the null right if you guys remember that's your rule remember the p-value really only tells you something about the null you have to sort of make an inference to make to say something about the alternative but the rule for high V value is we fail to reject the null in other words I don't have evidence to reject a null but if the null was the claim then you don't have evidence to reject the claim does that make sense and the conclusion you have to it you can't just say null and alternative you have to say claim you have to kind of think about what the person actually said or what the person asks you to figure out as the statistician or the data scientist so if we kind of look at that right so I if it was a high pvalue and the claim was the null hypothesis I would say there's not significant evidence to reject the claim okay that means the claim could be correct but I don't really have evidence to evidence to prove one way or the other okay now what happens if the claim is H a okay so again we got a low p-value right if we have a low p-value from some unbiased sample data that would consider it significant evidence and it means that we can reject the null hypothesis right we think the null hypothesis might be wrong but if the if the null is wrong then the AJ might be correct right so we might be supporting H a so a low p-value tells you again that you can reject the null but you're also supporting H a so if H a was the claim if the person in the article said a statement that was the alternative hypothesis then we can support that claim this is also kind of what everybody and a hypothesis test is looking for they like this one a lot they want to make the claim H a and they're hoping they're gonna get a low p-value from some good data and that's going to give them significant evidence to support the claim so that's the only time you really can support the claim and you have evidence to back it up so again a claim AJ AJ and a low p-value would tell me there is significant evidence to support the claim I think the claim is correct what that person said in the article and I have evidence to back it up okay all right what about this one so what if I have a high PE value in the claim is AJ okay this is the tricky one right so a high p-value means it could be sampling variability so we're not really sure if the null is wrong if the null might be correct and then it's not evidence either so so if I if I don't know that the null is right or wrong I sort of don't know if AJ is right or wrong so so a high p-value in the claim a che we would say there's not significant evidence to support the claim it's kind of a not support since a situation so in other words the claim might be wrong but I really don't have evidence to back it up so it's a not support situation all right the claim might be wrong but I don't have evidence okay that's kind of the idea so these are sort of the four conclusions you can write okay depending on what your situation you're dealing with all right so let's look at a couple examples here so here's our first example we're looking at the population mean body temperature this was sample data that I got off a stat key remember we kind of have used this example in the past and again my null hypothesis was that the population mean body temperature is 98.6 degrees Fahrenheit the alternative hypothesis was that the population mean mu is less than 98.6 degrees Fahrenheit and that's what many scientists believe that the population mean body temperature is actually less than ninety eight point six when I was growing up they always said it was ninety eight point six but nowadays we kind of think it's lower so that's my claim that's what we think is true we actually don't think it's still might be point six we think it's less than ninety eight point six so that's my claim it's important to know when you're right in conclusion is what's the claim was the claim the nola was the claim in each a that's really important now I got my p-value in my significant