all right in this video we are continuing with our hypothesis testing from chapter 10 and in this video specifically instead of using our classic hypothesis testing method we're going to talk about hypothesis testing with P values so I'm going to skip through the first page um all of this is the same as last time except in the last video we looked at test statistic versus critical value I told you there was this other method where you looked at P value versus significance level and that is what we are talking about in this video so not test statistic not talking about this part we're focusing on understanding our P value all right so we're just going to jump into examples this example is the exact same as the last video so I'm going to copy over some information from the last video um we ended up finding that our hypothesis was mu = to 70 and mu greater than 70 and we found our Z test statistic is equal to 2.02 so now what we need to do is using that test statistic we need to find our P value so our critical value that we talked about last time pairs up with our significance level which is our Alpha so we can kind of estimate with an alpha of 0.05 we kind of know where 05 falls on our curve it's going to be somewhere around here this is because we've done this for so long that we know this is Alpha equal to 0.05 we know kind of what 0.05 looks like when we shade it and this is our reject region and then we have our do not reject region and remember we shaded to the right because we have a one-sided upper tail test and then we found our test statistic of 2.02 so our test statistic will give us our P value and our P value is our area under the curve towards the reject region from our test statistic so I need to use my 2.02 Z value to find the P value that's going to be equal to the probability that Z is greater than 2.02 so that's the area under my curve from my test statistic towards my reject region so that's that greater than all right so now I go to my Z table I'm looking for 2.02 so 2.0 two is going to be this number here and remember my Z table gives me everything to the left but I want everything to the right so I need to do 1 minus 9783 and that is equal to 0.0217 and so I'm going to draw my P value on my curve now and that's going to be somewhere around here I'm going to say P value is equal to 0.0217 and so not only can I see in my curve that I'm falling in my reject region but what I also can take away from this is my P value is less than Alpha so I have less shaded region for my P value than I do for my my reject region which is Alpha therefore I reject H sub so then I would go on and give my full conclusion like we did in the last video it would end up being the exact same so if you want to refresh on that look back to your notes from the last video and so what we can see here is we're told reject if our P value is less than our significance level and do not reject if our P value is greater than our significance level so now let's do another example again same example from last video and to copy over some things we found our H subow was mu1 minus mu2 greater than 2 and H1 was mu1 minus mu2 oh I did that backwards it should be equal to null hypothesis is always equal to two and this one is greater than two and then we found our T test statistic equal to 1.04 and we found our reject region is based on our 05 level of significance and again we have an upper one-sided so somewhere around here is going to give me reject with Alpha equal to 0.05 and this is my d reject region so now I need to find what my P value is for this T value so my P value is going to be equal to the probability that t is greater than 1.04 and remember we had a degrees of freedom equal to 20 so T greater than 1.04 and I'm using greater than because that relates back to the test I'm doing and thus my reject region so now I need to go to my T table I'm looking for for 1.04 at 20 degrees of freedom so with the T table again it reads to the right so it's reading the right direction that we want great and I have to stay in my degree of Freedom row there's absolutely no question I am going to pull a number from this section so I'm looking for 1.04 in here it doesn't exist it's somewhere between these two numbers and it's way closer to this one than the other so I'm going to take this number which corresponds to A P value of15 so we're going to say it's approximately 0.15 and so I want to shade on my curve where I have about 15% so I'm going to go I don't know somewhere around here and say P value equal to 0 15 and so now you can see again that my P value is in my do not reject region that's where it falls and so I have P value greater than Alpha therefore do not reject and so then I want to give my full conclusion statement again but like I said you can look back to the previous video and copy that down so in this video we compared our P value to Alpha in order to draw our conclusions in the last video we compared our critical value to our test statistic so we need to keep that in mind let me see if I can draw a figure here so critical value relates to test statistic so and then we have our Alpha that relates to our P value so our so we compare in this Direction Compare these two and our critical value is approximately equal to our Alpha and our test statistic is approximately equal to our P value and I say approximately equal just because they are directly related to one another like if you have your test statistic you can find your P value if you have your P value you can find your test statistic same with critical value if you have your critical value you can find your Alpha and if you have your Alpha you can find your critical value very very directly this comparison between is what gives us our conclusions this is how we determine our reject or do not reject State all right one other super quick thing to note um in the videos my concept sheets do not have your proportion equation you will have them in class just I didn't get them into the video but that's okay all right if you have questions we'll cover them in class and I'll talk to you then