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## AP®︎/College Statistics

### Unit 10: Lesson 3

The idea of significance tests- Idea behind hypothesis testing
- Examples of null and alternative hypotheses
- Writing null and alternative hypotheses
- P-values and significance tests
- Comparing P-values to different significance levels
- Estimating a P-value from a simulation
- Estimating P-values from simulations
- Using P-values to make conclusions

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# Examples of null and alternative hypotheses

AP.STATS:

VAR‑6 (EU)

, VAR‑6.D (LO)

, VAR‑6.D.1 (EK)

, VAR‑6.D.2 (EK)

, VAR‑6.D.3 (EK)

, VAR‑6.D.4 (EK)

, VAR‑6.D.5 (EK)

, VAR‑7 (EU)

, VAR‑7.C (LO)

, VAR‑7.C.1 (EK)

The null and alternative hypotheses are both statements about the population that you are studying. The null hypothesis is often stated as the assumption that there is no change, no difference between two groups, or no relationship between two variables. The alternative hypothesis, on the other hand, is the statement that there is a change, difference, or relationship.

## Want to join the conversation?

- Does the null hypothesis need to have the equality symbol only?

In the second question about average hours of sleep, Sal writes the null hypothesis H0: u >= 8 hours. However, in every other null hypothesis I've seen on Khan Academy, the null hypothesis has a "=" not a ">=" or "<=". Is it required to write only "=" or are the other two equality symbols okay as well?(7 votes)- The short answer is
**yes**: the other symbols are fine. It really depends on your research question or the test you conduct.

Your null hypothesis is simply what you assume to happen at baseline when everything is going as it should be. Often, this means no difference, which is the same as equality, =.

But you could be comparing reviews of popular American movies in, say, Russia. Consider*Avatar*(2009), the highest grossing American movie of all time. It is reasonable to*assume*, at baseline, that*most*Americans would rate Avatar favorably. But do Russian sensibilities differ significantly?

How we approach this question (one-sided or two-sided) depends on how we articulate our hypotheses.*If*we have evidence that Russian ratings of American movies tend to be lower than American ratings of American movies--maybe we read studies about this trend, or observed it while surfing the Internet--then our hypotheses would be:**Null**: Russian ratings < American ratings**Alternative**: Russian ratings >= American ratings

But maybe we have no clue how Russians rate American movies. If the ratings were the same, then that would not be a very interesting finding, right? Equal ratings mean that the film was good. But*if*we found a difference in ratings, that could be interesting because now we have a new question: why are the ratings different? But before we get ahead of ourselves, it is possible to frame the hypotheses as statements of equality:**Null**: Russian ratings = American ratings**Alternative**: Russian ratings =/= American ratings

So, yes: you can use logical comparisons beyond simple equality. It depends how you frame your research question.(17 votes)

- Helloo.

Can someone help me to explain how null hypotheses works. I don't understand? I need help urgent.(0 votes)- The null hypothesis is what happens at baseline. It is the uninteresting hypothesis--the boring hypothesis. Usually, it is the hypothesis that assumes
**no difference**. It is the opposite of your research hypothesis.

The alternative hypothesis--that is, the research hypothesis--is the idea, phenomenon, observation that you*want to prove*.

If you suspect that girls take longer to get ready for school than boys, then:**Alternative**: girls time > boys time**Null**: girls time <= boys time

If you think that your sibling gets more expensive presents than you on the holidays, then:**Alternative**: sibling presents cost more than my presents**Null**: the cost is not different

I think of null as not, nothing, void, absent, uninteresting, normal, not worth reporting. If the null hypothesis were true, and you explained the null hypothesis to a friend, they might say, "Well, duh! Who cares?"

Imagine going up to your friend and saying, "I had to reject the claim that my sister gets more expensive presents than me around the holidays! It turns out that my parents treat us the same!"

Your friend: "Well, duh! Who cares! Parents are*supposed to*love their kids equally."

The null hypothesis is the who-cares hypothesis.(22 votes)

- Sal said 'lets remind ourselves what null hypothesis is' did he cover this topic somewhere else?(2 votes)
- ha ha, not at least in this segment earlier.(9 votes)

- At the second question didn't the statistics class assume that the average sleep time at their high school is less than 8 hours?(4 votes)
- shouldn't the null and alternative be mutually exclusive and collectively exhaustive? If H0 is =, then H1 can only be ≠. To test if H1 is "<" then H0 has to be ≥.(3 votes)
- Yes, it has to be one or the other. Several of the examples in the video can be neither.(1 vote)

- It's such an abuse of language to suggest that your so-called hypothesis is the exact thing you think is false. If you suspect they're sleeping less than 8 then obviously your hypothesis is not that they are sleeping 8 or more. Don't worry, I understand just fine; I just don't respect it and won't be able to respect anyone who uses this statistical language for the rest of my life.(2 votes)
- What happens if we interchange null and alternate hypothesis? How does the test change(2 votes)
- It doesn't change the test but it reverses the result you get at the end. Ex.) You would reject the Ho instead of failing to reject it or vice versa.(1 vote)

- What is the meaning of simulation given in the previous exercise of simple hypothesis testing. I am not able to capture the idea of frequency given in the simulation table.(1 vote)
- How would I find the level of significance for weight loss using 12 individuals 6 loss more weight(1 vote)
- Anybody else think it's weird our null hypothesis for the second example is based on a recommendation stating teenagers should sleep >=8hrs. It doesn't say they do.

I thought the point of null hypothesis and alternative hypothesis was to challenge established ideas. So if we had an established population average of teenagers sleeping >=8hrs of sleep, that'd be the null hypothesis that someone could go and challenge with their alternative hypothesis. The idea of setting up a null hypothesis from a recommendation and not an actual statistic throws me off.

Any thoughts?(1 vote)

## Video transcript

- [Instructor] 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? And 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, this 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 a value
where the value is what people were kind of assuming all along. The alternative hypothesis, this 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. And so in this context, the no difference, we would say the null hypothesis would be, we would care about the
population parameter, and 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. And then the alternative hypothesis, this is what the owner fears, is that the mean actually
might be larger than that, larger than 530 milliliters. And 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, and in this case we're
talking about estimating the population parameter,
the population mean, for how much drink is
dispensed on that setting. And 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 says the mean is
greater than 530 milliliters, and that indeed is the owner's fear. And this over here, this
alternative hypothesis, is that the, that it's
dispensing on average less than 530 milliliters, but that's not what
the owner is afraid of. And so that's not the kind of the 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, the mean from the 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. So the null hypothesis is, hey there's actually no news here, that everything is what
people were always assuming. And so the null hypothesis
here is that no, the students are getting
at least eight hours of sleep per night. And so that would be, that remember we care about
the population of students. And so and we care about
the population of students at the school. And so 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. And 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, so they suspect that
things might be different than what people have always been assuming or actually what's good for students. And so they suspect that
students at their school are getting less than eight
hours of sleep on average. And so they suspect that
the population parameter, the population mean, for
their school is actually less than eight hours. And 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 wanna 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.