so you probably want to pause the video so you have time to copy down this problem for your notes but unpause when you're ready so we have a claim here a claim from a chamber of commerce representative and so as we read through the claim our job is going to be in order to conduct hypothesis testing our job is going to be write the claim in symbols and then we'll identify whether it is a null or an alternative hypothesis so the claim is about temperatures and they're claiming that the the um mean temperatures here in the summer is 82° so we're we're focusing in on that keyword is it doesn't say less than greater than it's just is so writing that claim in symbols and I always just use the variable X when I write my claims your book I notice we use a different variable depending on the wording but I just use the variable X is is just an equal bar again it's not less than or greater than it's just they're saying X is the mean is 82 by the way I don't have my stylist with me so I'm using my finger so it's all wonky so hopefully you'll forgive me okay that's the claim so I'm going to label it as the claim well that looks really bad all right well next thing we're going to do is write the compliment so we have a claim written we're going to write the compliment of that which would be what are all the other options well the other option is that X does not equal 82 we don't see less than we don't say greater than because it could be either or so that's our complement to X equals and now our job is to identify which is the null and which is the hypothesis we look at one thing and one thing only which of those two symbols has an equal bar well this one has the actual full equal sign so that automatically makes it the null hypothesis which means the other symbol is our ha our alternative hypothesis statement so we have identified the null which we symbol is ho o or ho yeah okay I know it's weird but that's what we do um NH ha is the alternative and now what we're going to do is determine whether or not when we go to do our testing whether we're going to do a left tailed right tailed or two-tailed test you only look at the ha it doesn't matter what the claim is it doesn't matter what the claim is you only look at the ha statement and you look at its symbol the not equal to symbol tells you that you're going to conduct a two- tail basically because you're going in two directions greater than and less then those two things together make up not equal to so here's our second example um those of you that are from the Tri Cities area they have speed cameras that they put up in a little city town called Piney Flats and they claim it's because there were a lot of accidents there and um you know I think really to be honest with you a bunch of us should go in there and do some some hypothesis testing but um so it might be that after the the cameras they wanted to do some uh analysis and they're saying that now there are at most most three accidents per month in Piney Flats well if we're going to do hypothesis testing we need we need to be able to put that claim in symbols so I've got to be really careful with the phrase atmost three the word most we usually associate with greater than but in this case it says at most which means that's the most they're saying you're going to have in any given month it could be less so that's at most three is actually the symbol X is less than or equal to three so it could be three that's why we have to put the equal bar but that is the most it could be so it could be less than it could be equal to but that's it uh so X is less than or equal to three again you can use any variable other than x you can use M or a for accidents what or or uh your book uses the mean symbol I think but anyway uh that's our claim and now what we're going to do is we're going to write the complement to that so the opposite of being less than or equal to is simply being greater than three that's the complement now we're going to identify which is the null and which is the alternative it has to do with only one thing and that's which of these symbols have the equal bar and there it is right there that one has the equal bar this one has no equal bar this one does so automatically that tells you that that is your null hypothesis that means again that the uh complement is ha your claim will not always be the null um it just depends on which symbol has the the equal bar so now let's talk about what type of test to conduct whether it's left tailed right tailed or two-tailed we only look at the ha statement the alternative not the claim not the ho but the ha always the ha um we look at the symbol X is greater than three if you think about that symbol as an Arrow it's pointing to the right so your answer would be we're going to conduct a right tailed test it's one tailed and that tail is actually we're interested in the area pointing to the right okay last one that we have on this example so we have a claim somebody's making more than 62% that's the language we're interested in that's our claim more than is a greater than concept so we're going to say x is greater than I'm going to put 62 because when we conduct our hypothesis testing we always convert percentages to decimals so um that's the claim so I'm going to write down I'm going to label that as the claim I'm going to write the complement the opposite of being greater than you can't just say less than 62 and the reason is because you're leaving out the equal option so if it's not greater than 62 it could be less than 62 or it could be equal to so the complement would be less than or equal to now your job is to look for which of those statements has the equal bar there is no equal bar with the claim this time the equal bar is down here in the complement so wherever the equal bar is that's the only thing you look at to determine whoa sorry everybody to determine that the null hypothesis this time is down in your compliment statement FM there and that means your claim is an alternative your claim in this case is an ha so sometimes your claim is the null sometimes your claim is the alternative it's important that you remember that now the next skill is determine whether it's right tailed left tailed or two-tailed uh I don't look I don't worry about which is the claim all I look for if I could borrow that Arrow nope I'll have to make another arrow all I look for is the ha here's my whoa here's my ha so I look for the ha I go to the symbol at the ha statement that arrow is pointing to the right so I know that I'm going to conduct a right tailed test again