 So one important terminology that comes up in hypothesis testing is one or two-tailed hypothesis tests. And that comes about as follows. Suppose you're trying to decide whether a coin is fair. You flip it ten times and observe it lands heads eight times. The question you've got to ask yourself is, do you feel lucky? And you might argue as follows. A fair coin should land heads about five times in ten flips. It's very unlikely a fair coin would land heads eight times in ten flips. So we'll conclude that this is not a fair coin. What's important to understand is your decision has set a precedent. More importantly, it sets up a way that we can decide other cases. So if seeing eight heads in ten flips causes you to reject the null hypothesis, you'd also reject the null hypothesis if you saw nine heads in ten flips or ten heads in ten flips. Once you reject the null hypothesis on the basis of one observation, any more extreme result should also cause you to reject the null hypothesis. These more extreme results are called detail observations. But wait, there's more. If seeing eight heads in ten flips causes you to reject the null hypothesis, what if you saw eight tails in ten flips? Equivalently, two heads in ten flips. Or if you saw nine tails in ten flips, one head in ten flips. Or ten tails in ten flips, which is to say zero heads in ten flips. But these observations are a tale of a different sort. They're just as extreme, but in some sense in the opposite direction. And so there's actually a second tale. And one of the important decisions we have to make in hypothesis testing is whether we have a one-tailed test or a two-tailed test. And as a general rule, use a two-tailed test. The only time you might even consider a one-tailed test is if it's impossible to obtain one extreme. Then we might consider using a one-tailed test. So, for example, if we're trying to decide whether a treatment increases the growth rate of plants, we'll grow five plants without treatment and five plants with treatment. And at the end of the experimental period, you measure the height of the plants should you use a one-tailed test or a two-tailed test. And again, the default answer is use a two-tailed test. And in this particular case, since it's possible for the treatment to reduce the growth rate of the plants, both extremes are possible, so we should use a two-tailed test. So suppose we have a machine that fills cereal boxes and it's set to deliver at least 16 ounces of cereal, and you want to determine if it's delivering more than this amount. Should you use a one-tailed test or a two-tailed test? And again, the default is you should use a two-tailed test. But in this case, it's set up as impossible for the machine to deliver less than 16 ounces of cereal. And so we should use a one-tailed test.