## How to Set Up a Hypothesis Test: Null versus Alternative

If you only want to see whether the time turns out to be greater than what the company claims (that is, whether the company is falsely advertising its quick prep time), you use the greater-than alternative, and your two hypotheses are

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How do you know which hypothesis to put in H_{0} and which one to put in H_{a}? Typically, the null hypothesis says that nothing new is happening; the previous result is the same now as it was before, or the groups have the same average (their difference is equal to zero). In general, you assume that people’s claims are true until proven otherwise. So the question becomes: Can you prove otherwise? In other words, can you show sufficient evidence to reject H_{0}?

## All null hypotheses include an equal sign in them.

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When you set up a hypothesis test to determine the validity of a statistical claim, you need to define both a null hypothesis and an alternative hypothesis.

## Statistical hypothesis testing - Wikipedia

Neither decision of rejecting or not rejecting the H_{0} entails proving the null hypothesis or the alternative hypothesis. We merely state there is enough evidence to behave one way or the other. This is also always true in statistics!

## Significance Tests / Hypothesis Testing - Jerry Dallal

The *p*-value represents **how likely** we would be to observe such an extreme sample if the null hypothesis were true. The** p-value is a probability** computed assuming the null hypothesis is true, that the test statistic would take a value as extreme or more extreme than that actually observed. Since it's a probability, it is a number between 0 and 1. The closer the number is to 0 means the event is “unlikely.” So if

*p*-value is “small,” (typically, less than 0.05), we can then reject the null hypothesis.

## Significance Tests / Hypothesis Testing

We rejected the null hypothesis, i.e., claimed that the height is not 65, thus making potentially a Type I error. But sometimes the* p*-value is too low because of the large sample size, and we may have statistical significance but not really practical significance! That's why most statisticians are much more comfortable with using CI than tests.

## Suppose someone suggests a hypothesis that a certain population is 0

Typically in a hypothesis test, the claim being made is about a population (one number that characterizes the entire population). Because parameters tend to be unknown quantities, everyone wants to make claims about what their values may be. For example, the claim that 25% (or 0.25) of all women have varicose veins is a claim about the proportion (that’s the ) of all women (that’s the ) who have varicose veins (that’s the — having or not having varicose veins).