[BLANK_AUDIO] There's a saying in English," to know something like the back of your hand", which means to know something very well. Myth Busters, a popular TV show, put to test the validity of the saying. They recruited 12 volunteers, each of whom were shown 10 pictures, of backs of their hands, while wearing gloves, so they couldn't actually see their own hands, and they were asked to identify their own hand among the ten pictures. Eleven out of twelve people completed the task successfully, meaning they were indeed able to recognize the backs of their own hands. What are the hypotheses for evaluating whether these data provide convincing evidence of the validity of the saying. In other words, that people do better than random guessing when it comes to recognizing the back of their own hand. Remember that for each person, they're picking between ten pictures, so if they were randomly guessing, their probability of success would be 10% or 0.1. They're doing better than randomly guessing, then their probability of success is greater than 0.1, and that's what would go in our alternative hypothesis. With such a small data set, we're not going to meet the success/failure condition, so we're going to need to turn to a simulation-based method to evaluate these hypotheses. So, in the next exercise, we're going to fill in the blanks in this description of how our simulation scheme can be set up. We want to use a blank-sided fair die to represent the sampling space, and we want to call a success, guessing correctly, and all other outcomes failures, guessing incorrectly. So remember, we have to assume that the null hypothesis is true, then what should be the probability of guessing correctly? Indeed we want a 10 sided fair die here because in our null hypothesis we are setting P equal to .1. Then we want to role the die blank times, each representing one of blank people in the experiment. We had 12 people in the experiment. So we want to roll the die 12 times for each representing one of 12 people in the experiment. Then, we count the number of rolls that resulted in ones because we had said that that's what we're calling a success. And we calculate the proportion of correct guesses in one simulation of 12 rolls. Let's say we're going to repeat this step 100 times, it's not a huge number of times but it's high. Each time recording the proportion of simulated success in a series of 12 rolls of the die. Finally, we want to create a dot plot of the blank proportions from step three, and count the number of simulations where the proportion is blank. Now, in this case, the proportions that we're collecting are simulated proportions. And in order to find the p-value, we want to find the number of, the proportion of proportions, where the observed outcome, or something more extreme, was observed, meaning that we're 11 out of 12 or greater number of people, guess their back of their hands correctly. This is our observed proportion, the 11 out of 12. We can actually run this simulation easily using R, and the inference function that we've been using in the labs. We want to first set up our data, so the back of the hand is going to be, we have 11 correct guesses, and one incorrect guess. And then we can feed that to our inference function where the first argument is the data set that we're working with. The estimate we're working with is a proportion. This is a hypothesis test. That's a simulation based hypothesis test where defining the success to be the correct guesses. And our null value was .1, and the alternative was greater. And for simplicity, for now, we're only going to run 100 simulations of this. This is what the output looks like. So we can see that we get a pretty small P value, and we can see from the distribution of the possible simulated proportions that it is quite unlikely to get 11 out of 12 right. Remember that 11 out of 12 corresponds to .9167. So the P value is basically the probability that P hat is greater than or equal to .9167. Given that the true population proportion is point 10 and it seems like it's almost zero.