Examples of null and alternative hypotheses | AP Statistics | Khan Academy

We are told a restaurant owner installed a new automated drink machine. The machine is designed to dispense 530 milliliters of liquid on the medium size setting. The owner suspects that the machine may be dispensing too much in medium drinks. They decide to take a sample of 30 medium drinks to see if the average amount is significantly greater than 500 milliliters.

What are appropriate hypotheses for their significance test? They actually give us four choices here. I'll scroll down a little bit so that you can see all of the choices. So, like always, pause this video and see if you can have a go at it.

Okay, now let's do this together. So let's just remind ourselves what a null hypothesis is and what an alternative hypothesis is. One way to view a null hypothesis is this: it is the hypothesis where things are happening as expected. Sometimes people will describe this as the no difference hypothesis. It'll often have a statement of equality where the population parameter is equal to the value, where the value is what people were kind of assuming all along.

The alternative hypothesis is a claim where, if you have evidence to back up that claim, that would be new news. You are saying, "Hey, there's something interesting going on here. There is a difference."

In this context, the no difference hypothesis, we would say the null hypothesis would be, we would care about the population parameter. Here, we care about the average amount of drink dispensed in the medium setting. So the population parameter there would be the mean, and that the mean would be equal to 530 milliliters because that's what the drink machine is supposed to do.

Then, the alternative hypothesis, this is what the owner fears: that the mean actually might be larger than that, larger than 530 milliliters. So let's see which of these choices is this. Well, these first two choices are talking about proportion, but it's really the average amount that we're talking about. We see it up here; they decide to take a sample of 30 medium drinks to see if the average amount. They're not talking about proportions here; they're talking about averages.

In this case, we're talking about estimating the population parameter, the population mean, for how much drink is dispensed on that setting. So this one is looking like this right over here. Only these two are even dealing with the mean, and the difference between this one and this one is this: this says the mean is greater than 530 milliliters, and that indeed is the owner's fear.

This over here, this alternative hypothesis, is that it's dispensing on average less than 530 milliliters, but that's not what the owner is afraid of. That’s not the kind of news that we're trying to find some evidence for. So, I would definitely pick choice C.

Let's do another example. The National Sleep Foundation recommends that teenagers aged 14 to 17 years old get at least eight hours of sleep per night for proper health and wellness. A statistics class at a large high school suspects that students at their school are getting less than eight hours of sleep on average. To test their theory, they randomly sample 42 of these students and ask them how many hours of sleep they get per night. The mean from this sample is 7.5 hours.

Here's their alternative hypothesis: the average amount of sleep students at their school get per night is... what is an appropriate ending to their alternative hypothesis? So pause this video and see if you can think about that.

So, let's just first think about a good null hypothesis. The null hypothesis is, "Hey, there's actually no news here that everything is what people are always assuming." So the null hypothesis here is that no, the students are getting at least eight hours of sleep per night.

So that would be, remember, we care about the population of students. We care about the population of students at the school. We would say, well, the null hypothesis is that the parameter for the students at that school, the mean amount of sleep that they're getting, is indeed greater than or equal to eight hours.

A good clue for the alternative hypothesis is when you see something like this where they say a statistics class at a large high school suspects. They suspect that things might be different than what people have always been assuming, or actually what's good for students.

So they suspect that students at their school are getting less than eight hours of sleep on average. They suspect that the population parameter, the population mean for their school, is actually less than eight hours.

So if you wanted to write this out in words, the average amount of sleep students at their school get per night is less than eight hours. Now one thing to watch out for is, one, you want to make sure you're getting the right parameter. Sometimes it's often a population mean; sometimes, it's a population proportion.

But the other thing that sometimes folks get stuck up on, but the other thing that sometimes confuses folks is, well, we are measuring, is that we are calculating a statistic from a sample here. We're calculating the sample mean, but that the sample statistics are not what should be involved in your hypotheses. Your hypotheses are claims about your population that you care about. Here, the population is the students at the high school.