Today is a top 10 topic number seven I keyvalue store probability is we are on the business are the 200 page book through exam review, and we will click on statistics show from statistics for two and open the PowerPoint presentation to and scroll down here to slide number 88 to 88 is the start of top 10 topic number seven okay peace value is going to score and a slight 89 here that the definition according to this for PowerPoint presentation is a pea values the probability of getting a sample statistic as extreme or more extreme than a means. Will as large or larger than the sample statistic you got from your own sample or the sample in the problem given that the no hypothesis is sure that's rather a long statement but if you remember a normal distribution with a curve in you or you're looking at details the pea values the probability of getting a sample statistic that's in the tales on either one of the tale will just call a one tail test or in either of the two tales, which is called a two tale tests show that the probability of getting that had probability of getting a sample statistic as extreme or larger war or moral extreme that means or larger than the sample statistic you got from your own sample. Given that the null hypothesis is Chu, which is to did it occur by chance. And that's usually something that we would not like we want to reject the idea that could have occurred by chance to scrolling down here to page 90 here's an example of the people got it on Mrs. and example of a hypothesis testing of how you test us. So people value example is a one tailed test were just looking at one side of the normal distribution for example to in the first bullet H. subzero or H. not sometimes called the no hypothesis the bet is that the mean of the population that you know that's new population mean is equal to 40 the alternate hypothesis, the one that you believe to be true or might be true it is that the meaning is greater than 40 so that's been skeptical of that and do it so one tailed test. Is this a direction and assign greater and third bullet you're given a little that of information in the sample mean is 43 bullet number for the P. value this really should rewritten in lower case. Rather than uppercase. But lower case be a sequel to the probability that's an upper case. If of the sample mean Green greater than a 43 and a day given that the no hypothesis is true so that the value is the probability that that sample mean is greater than 43 given that the null hypothesis is true below point number five. What's the meaning of that sentence above is a probability of observing of of of observing a sample as large as 43 when the population mean is $.46 on the null hypothesis. So what's the probability of observing a sample mean as large as 43 when the population means 40 UK remember the sample is to did it to half the population. This is is generally typically unknown cuts, will we have to test the of a populist contest of a less bullets had a use that we reject the no hypothesis if the P. value is less than a. That's a little symbol here at the end. A is the significance local for example like .05 for example the paint so we reject the no hypothesis which would mean that we can except the alternate hypothesis or report least it if we if we can read it with and if we can't reject on all hypothesis weak weak weak and say that though we fail to accept the no hypothesis which it gets us a little closer to being able to accept that the alternate hypothesis, which is really what you want, so we would like to reject the no hypothesis saying that the mean is equal population musical before he is the key value is less spam comp .essay .05 for example you'll be given that in the problem is not given that you can assume .05, but you'll be given us the level of significance that the significance level in the problem case slide number 91 for example two different cases suppose the probability. That a there that Wilson mostly Greek letter lowercase Greek. Or a suppose a is .005 (case number one suppose that the value is equal to .02. Okay, that's that's that's that's the probability that I then you would reject the null hypothesis because all .02 is less than .05 okay in other words, it's unlikely that. So it's it is on. It is unlikely that the no hypothesis are sure you believe that's your alternate hypothesis that the population mean is greater than 40 and tank right and that's the deaths how almost as science advances is we try and reject the idea of the no hypothesis that it could have occurred by chance. And if we can do that that gives us a little bit more support that the men that the alternate hypothesis age of a is true or is likely to be true to a case number to suppose you compute the pea value refined or you're given that the P. value is point away .0 wait is greater than .05 then you cannot reject the null hypothesis, the null hypothesis might be true with saying. You have reason to believe that the population may be greater than 40 tank you cannot recharge the null hypothesis in that particular case of a pain to be value is greater than .05, which is which means a at the probability could have occurred in the excuse me that it is that you're reasonably the population mean maybe 40 and not greater than 40 which means you cannot reject the idea that it's greater than 40 changes are two different cases. Here's an example was to tail to us to remember we did one tail to test before us is see whether or not is greater than 43 here's an example of a two tail test for the no hypothesis is that the population mean is equal to 70. The alternate hypothesis is that the population mean is not equal to suffer me not just greater than 70 or less than 70 but either greater or less and 70 just some number other than 70 years of example. Say of a sample mean of 72, if it's a two tale tests for example in the P. value is two times the probability of the sample mean is greater than 72, which is two times .04 and he which is equal to .08 okay because were looking on both sides of the normal distribution, not just one side if the probability of the alpha value if the level of significance and significance level is .05 probability value is greater. Than a, so you don't reject the no hypothesis and we would we would like to reject the hypothesis if we can only cant in this particular case because point though a probability value is greater than .05 and you'll be given those those numbers in the problem of cake that makes it easier. It's easier to draw a normal distribution for the paying draw two lines on the distraught to vertical lines at the point save for a .05 distribution, and then color in different sides either the except region or the reject region. And then you'll know whether or not to accept or reject it to reject regions are on the Anderson on the tails to accept regions are in the middle name. And that's top 10 topic number seven