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This is the form of a hypothesis test when we do a hypothesis test we start out with a null hypothesis we typically read it this way h4 hypothesis zero for that no and we write the null hypothesis either in English or using mathematical terms but we might say something like the null hypothesis is that the lady does not let's see I'll say the lady does not have this skill there's multiple ways to phrase it maybe she doesn't have the skill of distinguishing between these two types of cups we come up with a null hypothesis an assumption if there's actually nothing real going on here no real pattern then we come up with what's called a test statistic some summary of our data that's just one number so here the lady picked out four cups that was our data and our statistic is the number of cups she got correct and then what we do is we come up with what's called the reference distribution that's what this is we'll put this on a slide in just a moment but I think it's helpful to label it here this is the reference distribution the reference distribution shows you each of the possible values of the test statistic what we'd see in the data and how likely those different values would be if the null hypothesis were true so remember how we got this histogram we said assuming the lady is guessing at random what's the probability she'd get each of these numbers of cups correct and then to finish the hypothesis test we look at what we actually saw so these are all the numbers of cups that she could have gotten right but suppose she actually got three of them right and then we say okay well looking at this histogram looking at this distribution how extreme is the value we actually saw and we calculate that by saying what's the probability we would have seen a value for example at least as big as we actually saw and here that's 17 out of 70 that's called the p-value we could have calculated this number in multiple ways what we calculated is called a right-sided p-value what's the probability that we would see a number at least as big we actually saw if the null hypothesis is true we also could have calculated the left sided p-value what's the probability she'd get three or fewer correct okay the definition of the one-sided p-value is just the minimum of those two which is smaller the probability should get something at least as big as three or the probability should get something three or less and by convention the two-sided p-value is two times the one-sided p-value let me put this on a formal slide for you so again here's our setup the lady claims that she can tell whether milk is poured into a cup before or after the tea is poured we have four.