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### Course: Statistics and probability>Unit 12

Lesson 1: The idea of significance tests

# Examples of null and alternative hypotheses

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?

• Sal said 'lets remind ourselves what null hypothesis is' did he cover this topic somewhere else?
• ha ha, not at least in this segment earlier.
• 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?
• 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.
• Helloo.
Can someone help me to explain how null hypotheses works. I don't understand? I need help urgent.
• 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.
• At the second question didn't the statistics class assume that the average sleep time at their high school is less than 8 hours?
• 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 ≥.
• Yes, it has to be one or the other. Several of the examples in the video can be neither.
(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?
• What happens if we interchange null and alternate hypothesis? How does the test change
• 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)
• On the sleep example, it seems the things being compared / tested are unrelated. The National Sleep Foundation RECOMMENDED a certain amount of sleep, saying nothing necessarily about how much sleep students regularly get, at least as presented. The statistics class is measuring something completely different, how much sleep students are actually getting.

How from that is the null hypothesis "Students are getting 8 hours of sleep per night?" when that isn't suspected by anyone?

By my understanding the null hypothesis is, "students are getting enough sleep". We could go further except that NSF doesn't qualify what "enough sleep" means ; graduation rate, test scores, physical health, self-reported well-being?