So, let's apply testing to a taste experiment. It's actually surprisingly difficult to distinguish Coke and Pepsi by taste alone, that means you're not allowed to see what's on the can. I did an experiment about this in a class at Stanford. We had 10 cups that were filled at random with either Coke or Pepsi. Then, a student volunteer tasted each of the 10 cups and correctly named the contents of 7. So, the question is, whether this is sufficient evidence to conclude that the student can tell apart Coke and Pepsi. So, what's the null hypothesis in this situation? Remember the generic expression for null hypothesis, is nothing extraordinary is going on. In this case, that would mean that the student does not have any special ability to tell Coke and Pepsi apart. In other words, the student would just be guessing. Now, we have to write this down in a way where we can introduce our methodology. So, we know that when we count things we will introduce 0/1 labels. So, in this case, we may have 1 for a correct answer and 0 for a wrong answer. Then, the null hypothesis would simply say that the probability of a correct answer is a half and the alternative would be that the probability of a correct answer is larger than a half. This is called a one-sided test, and that simply means that the alternative hypothesis is on one side of the null and not on both sides. So, in this case the z-statistic looks exactly like the one we had for coin tossing. We have an observed sum which is 7, the expected sum in 10 trials would be 5, and then we have the standard error of the sum in the denominator and we found that to be 1.58. So, the z-statistic comes down to 1.27. So, next we have to find the p-value. So, we have a standard normal curve, and we look at a z-value of 1.27, and the area to the right turns out to be 10.2%. And remember, we do a one-sided test, so we're not going to trouble with that one. And finally, the conclusion is since 10.2% is not smaller than 5%, we don't reject the null hypothesis. So, there's not enough evidence to convince us that the student can distinguish Coke and Pepsi. For this experiment, it might actually be also appropriate to do a two-sided test. That is, we would look at the alternative that the probability of a correct answer is different from a half. This alternative would correspond to a student who can distinguish Coke and Pepsi, but who may confuse which is which. For example, such a student might get one correct answer. So, very few correct answers are actually evidence that the student can distinguish Coke and Pepsi but he would mix up the two, and that actually happened once when I did the experiment. In general, you have to think carefully ahead of time, whether the alternative should be one-sided or two-sided. Keep in mind that for a two-sided test, the p-value gets doubled. If one does a two-sided test and it's not significant, then it may be tempting to declare that one wanted to do a one-sided test in the first place, and cut the p-value in half to get it under the 5% threshold, that is not okay. So, you have to declare ahead of time, whether you want to do a one-sided test or a two-sided test.