hi everyone this is Matt to show and intro stats and today we're looking at the topic of the null and alternative hypothesis so we're looking at introducing the start of hypothesis testing so it's a new unit for us we're kind of getting into this idea of a hypothesis test and and how that works out so let's get started so let's start with this idea of a hypothesis test since this is what our whole this whole unit is about hypothesis testing so think about hypothesis test as a procedure for testing a claim about a population so people oftentimes say things about the population all the tournament newspaper articles in magazine or online articles they're always saying things about what they think is true about what's going on out there in the world around us but how true is what they're saying I mean is they're saying is is what they're saying in the article could be true or is it really wrong hypothesis test is a procedure for determining or testing a claim about the population it also gives us a way of judging evidence how much evidence do we have for for what they're saying so but it is a quite a long procedure hypothesis test does take a quite a few steps I can't teach it to you sort of in one day you know I have to sort of do little steps at a time so we'll kind of be learning the basics of the pieces of hypothesis test and the eventually will get to the point where we can put all the pieces together and actually do a hypothesis test from start to finish okay so when you're talking about a hypothesis test one the first things you want to identify is what's the claim right what did the person say about the population or what does the person think is true about the population so our population claim what someone thinks is true about the population so when they're reading the article or reading something and they say something about a population they actually think is true now sometimes they'll give you an opposing view and sometimes they don't but we basically want to identify what was the claim what was the person what did the person think was true about the population now so let's take a look at these ones real quick and see if we can kind of figure out what the claim is that's always the start what's the claim right so what's the claim okay so this one says example says a population percentage of people that have side effects to a medicine used to be 4% now we think it's higher so let me ask you a question which of the two they said it used to be 4% but now they think it's higher which one do they actually think is true right right now do they think it's still 4% or do they think it's higher sounds like they think it's higher right the the population who used to be 4% again if sometimes if you read just the first sentence of an article or something you might have a wrong view about what their claim really is always read the whole thing before you try to decide what their claim is what do they really think is true sounds like they think that it's higher so I'm gonna write population percentage would be a population proportion so we could use P for population percentage or we could use PI my classes use pi so pi is higher higher means greater than greater than 4% so again I'm going to write that as a decimal and that would be my claim so I usually what I like to do is I write the word claim next to it claim okay so being able to identify what do they actually think is true now a couple things about this that I want to mention when you're doing a hypothesis test always put if you're doing a one population hypothesis test always put the letter on the left side and the number on the right side yes I know mathematically saying that point zero four is less than PI is true but it would this is not the way that's not the way pure programs are set up the computer programs for one population are always set up with the letter on the left and the number on the right and you do want to write a greater than a greater than it looks like an arrow pointing to the right and if you notice that it looks like the the tip of an arrow pointing to the right so greater than or higher or increase should always be a greater than pointing to the right again the letter the population parameter on the on the left and the number on the right so that's important with the way you write it because this is the way the computers are going to interpret it look at another claim many people thought that the population mean average normal body temperature was is 98.6 evidence now suggests it is lower hmm okay so kind of another thing right if I just read the first sentence I may think oh my claim is 98.6 but I don't think that's what they really think is true they kind of think that it's lower right it used to be ninety eight point six when I was growing up people always told me that but normal body temperature was not eight point six but now evidence now suggests that it's lower so it sounds like they think it's actually lower so that would be less than now this was a population mean average if you remember the letter for population mean average it's the Greek letter mu and Greek letter mu in our last chapter we talked about some of those famous letters and stats the Greek letter mu kind of looks like a U with a little tail on the left and it's less than or lower so less than looks like an arrow pointing to the left that's a good way to remember it and 98.6 this is not a percentage this is degrees Fahrenheit so again I want to go ahead and leave it as 98.6 don't try to mess with that it's not a percentage that you need to convert this is quantitative data and again I noticed I wrote the I wrote the letter on the left and the number on the right for one population okay all right so now we got this would be our claim right our claim okay what about this third one here so it says standard IQ tests have a population mean average of 100 all right standard AI population mean an average of 100 okay but that's it that's all they said standard IQ tests have a population mean average of 100 okay well it didn't say this must be the claim if that's the all they said right so let's think about it for a second okay well they didn't say more than 100 didn't say at least 100 and say at most 100 and say less than 100 right it just said 100 so that's like as classic equal to claim so sounds like again they're using a population mean average so it's the Greek letter mu again so mu is equal to 100 again that's going to be my claim that's what they they think is true okay so a claim is what you have to read it and kind of figure out what do they think is actually true about the population now from this claim we can now develop the null and alternative hypothesis okay always try to do your claim first though before you try to figure out the null and alternative hypothesis so in null hypothesis so in all that process is a statement about the population that involves equality it also can be a statement about no change no effect or no relationship those things really go with equality though if you have if you have equal to sort of shows not related we'll kind of get that into that later the alternative hypothesis a statement about the population that does not involve equality so not something that does not have an equal to part it can also be a statement involving there is significant change or significant effect or there is a relation that's always an 8 an alternative hypothesis now obviously we don't want to write null hypothesis over and over again or alternative hypothesis over and over again so we have symbols so the symbol for a null hypothesis again a statement about the population that has an equal to part would be h0 they put a little zero capital H with a little subscript zero next to it so H naught or H zero is the null hypothesis the alternative hypothesis a statement about the population that does not have equal is again denoted by sometimes as in capital H with a tiny little subscript a next to it some step books you'll see it as a H for the little one next to it so it could be H a or H one depending on what step up you're looking at I prefer a J I usually use H a in my classes okay so how do I figure out what's the Nolan what's the alternative okay well again one of your sort of the the steps to kind of doing a figuring this out always write down the claim first now try to figure out the opposing view sometimes in the in the article that will actually tell you the opposing view or sometimes you may have to use opposites so we might talk a little bit about opposites right now the opposite of less than I know some of you are out there saying you know greater than no the opposite of less than is actually not greater than the opposite of less than is actually greater than or equal to okay so it has to have that one of them has to have an equal to part the opposite of greater than number greater than points to the right is less than or equal to and of course the opposite of equal to is not equal to so what we saw here is the these ones over here all alternative hypotheses because they don't have an equal to part so a less than a greater than or not equal to is always an H a equal to or anything with equal to a less than or equal to greater than or equal to would be considered a null hypothesis though most of the time for a null hypothesis it's equal to people rarely use less than or equal to a greater than or equal to okay so let's take a look at these again so we said we found our claims now so let's see if we can find the opposing view what's the opposing view to the claim okay well let's really get population percent of people that have a side effects used to be 4% now we think it's higher so it sounded like here that the the opposing view was that it's 4% notice they never thought it was lower than 4% they all what they just thought it was 4% and now they think it's higher so it sounds to me like the opposing view would be equal to 4% so maybe our our posing view here would be pi equals 0.04 okay so it sounds like those are my two opposing views the one they think is true was the higher the greater than so I put claim next to that okay now I should be able now to figure out what's the null and what's the alternative remember the alternative is a statement that does not have an equal to part a null is a statement that has an equal to part so it has nothing to do with claim it has to do with these signs so the equal to one has to be the null hypothesis so I'm going to write that down that's got to be the null hypothesis alright let's do that so this one would be the null hypothesis I mean think I need a little more room here give myself a little