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Hypothesis Testing

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This tutorial covers hypothesis testing. Hypothesis testing is a very common procedure in making inferences. First off, what's a hypothesis? This might be a word that you've heard in common language or in a science class. When talking about statistics, a hypothesis is a claim about a population parameter.

So the key about a hypothesis is that you're making a claim about the population. So that's the key. It's only a claim. It's not something we know to be true. It's something we believe or are trying to prove is true, and it's about the population. An example could be a college president claiming that 75% of the athletes graduate in four years.

So the population they're talking about there is the athletes, and the claim they're making is that 75% of them graduate in four years. Now, a hypothesis test considers the probability that a sample statistic is equal to or more extreme than it could come from a population with a particular parameter.

So our example will help to make sense of that. It says, we take a sample of 30 student athletes and find that 18 graduated in four years. So we would want to test whether or not-- for that sample, how likely is it that it comes from this population, or that it could come from a population where 75% graduate in four years?

One are doing a hypothesis test, first we set up a null hypothesis. The null hypothesis is the starting assumption. It's the default. It's the no change, and it's a claim about a particular value. So for example, in the last one, our null hypothesis is that the population proportion is 75%. So the population proportion equals 0.75.

Now, this here is how we write null hypothesis. The H is telling us a hypothesis, at that 0 that's in subscript is telling us that it's the null hypothesis. The reason that's important is because there's another kind of hypothesis, the alternative hypothesis.

The alternative hypothesis is the other one. It's the one that's saying it's a claim that the population differs from the value claimed in the null. So whatever happens in the null, the alternative is saying that it's different. Now, you can say that it's less than, greater than, or just that it's not the same, that it's not equal to. So for example, we want to say that our alternative hypothesis is that the population proportion is not 75%. So we say P does not equal 0.75.

If we had reason to believe that the population proportion was less than 75%, we could have done that our alternative hypothesis is that the proportion is less than 0.75. So again, it's for a particular value. And you use the same kind of notation. This H with a subscript of a is telling us it's a hypothesis-- it's the alternative hypothesis.

One important thing to note is that the null hypothesis is always written as an equality. While the alternative hypothesis can be written as an inequality, the null hypothesis is always, always, always in equality. Now, when you're doing hypothesis testing, you're going to end up using statistics, and particular forms of statistics. We'll see more about that in other tutorials.

But when you're doing those statistics, the only thing you can do is reject or fail to reject the null hypothesis. You cannot accept the alternative hypothesis, because you're only testing the null one, so you're only testing whether or not you can accept and say, yes, 75% of that population is likely to graduate in four years.

You can reject that if your test shows that's not true, but you cannot accept the alternative hypothesis. That's one common error that people make, so beware of that-- that when you're drawing your conclusions during a hypothesis test, you're only accepting or rejecting the null. You're not talking about the alternative. This has been your tutorial on hypothesis testing.